Math is EDUCATIONAL!!

To find the square root of a number all you need to do is to look for a number when multiplied by itself, which gives you the number that you are rooting.  Square roots and squares are opposite operations, so if you now your square numbers well enough, square roots should be straightforward to carry out.

Example 1

Find the square root of 64.

So we are looking for a number when multiplied by itself that gives 64.

The number we are looking for is 8, because 8 × 8 = 64

Example 2

Work out √49.

The symbol that is before 49 is basically a square root sign. So we need to find the square root of 49.

Again, try to think of number when multiplied by itself gives 49.

The answer is 7, as 7 × 7 = 49

Example 3

Work out √9.

All you have to do is the same as before, and look for a number when multiplied by itself which gives 9. Be careful not to square 9, as this gives 81.

The answer is therefore 3 as 3 × 3 = 9.

Sometimes we will need a calculator to find a square root, as our answer will not be a whole number.

Example 4

Work out the square root of 157.

Well we know that, 12 × 12 = 144 and 13 × 13 = 169, so our answer is going to be a decimal answer somewhere between 12 and 13.

In order to work this out, we will need a calculator (just use the root button √)

So the √157 = 12.53 (2 dp)

Extra Tips

To find the square root of a number all you need to do is look for a number when multiplied by itself which gives you the number that you are rooting.

Make sure you are rooting the number, and not squaring the number! When you are square rooting a number, the answer is always going to be smaller than the number that you started off with.

You won’t be able to square root a negative number.

The square root of 1 is 1.

In this article I will explain how you can carry out Pythagoras’s Theorem without using the formula (a² + b² = c²). Pythagoras’s Theorem can be used to find a missing side length in a right angled triangle providing you know the two other side lengths. To do this follow these steps:

Step 1: Identify whether or not you are finding the longest side of the right angled triangle or one of the other shorter side lengths. This step is the most important!

Step 2: Take the square of your two numbers (multiply the number by itself).

Step 3: If you are finding the longest side of the right angled triangle add the two squares together (answers from step 2). If you are not finding the longest side take the two square numbers away.

Step 4: Square root the answer from step 3.

Example 1

In a right angled triangle (ABC) AB = 7cm and AC = 4cm. Find the length BC.

Step 1: BC is the longest side of the right angled triangle.

Step 2: 7 squared is 49 (since 7 × 7 = 49) and 4 squared is 16 (since 4 × 4 = 16).

Step 3: 49 + 16 = 65 (add them together as you are finding the longest side)

Step 4: The square root of 65 is 8.1 cm.

Example 2

In another right angled triangle (DEF) DE = 11 cm and EF = 13 cm. Find the length DF.

Step 1: DF is the shortest side length of the right angled triangle.

Step 2: 11 squared is 121 (since 11 × 11 = 121) and 13 squared is 169 (since 13 × 13 = 169).

Step 3: 169 – 121 = 48 (take them away as you are not finding the longest side)

Step 4: The square root of 48 is 6.9 cm.

Example 3

A ladder of length 15 m rests up against a vertical wall. The distance from the foot of the ladder to the foot of the wall is 2m. What is the distance from the bottom of the wall to the top of the ladder?

Step 1: The vertical distance up the wall is one of the shorter sides of the right angled triangle.

Step 2: 15 squared is 225 (since 15 × 15 = 225) and 2 squared is 4 (since 2 × 2 = 4).

Step 3: 225 – 4 = 221 (take them away as you are not finding the longest side)

Step 4: The square root of 221 is 14.9 m.

More Help:

More mixed Pythagoras questions.

Longest side Pthagoras questions.

Shorter side Pythagoras questions.

Rounding your numbers to 3 significant figures is probably one of the most popular ways of rounding off. To round to 3 significant figures follow these steps:

Step 1:

Count 3 digits from the left hand side of you number. Don’t count the zero’s at the start of the number.

Step 2:

If the digit to the right of this number is 5 or above – round it up.

If the digit to the right of this number is less than 5 – round down (keep it the same).

Step 3: Once rounded, keep the size of the number, by filling in zeros up to the decimal point. If you are already past the decimal point then don’t fill in zeros.

Let’s look at some examples:

Example 1

Round off 48362.9 to 3 significant figures.

First identify your 3rd significant figure (underline this)

48362.9

The number to the right of 3 is 5 or above, so round the number up to 484.

Now all you need to do is fill in zeros up to the decimal point.

48400

Example 2

Round off 912827 to 3 significant figures.

First identify your 3rd significant figure (underline this)

912427

The number to the right of 3 is 5 or above, so round the number up to 484.

Now all you need to do is fill in zeros up to the decimal point.

The number to the right of 2 is 4, which is less than 5. This means you round the number down (keep it the same 912)

Therefore, the required answer is 912000.

Example 3

Round off 14.738 to 3 significant figures.

First identify your 3rd significant figure (underline this)

14.738

The number to the right of 7 is 3, which is less than 5, so round the number down to 14.7.

There is no need to add zeros as you have already gone past your decimal point.

So the final answer is 14.7 to 3 significant figures.

Example 4

Round off 0.00019386 to 3 significant figures.

First identify your 3rd significant figure (underline this)

0.00019386

The number to the right of 3 is 8, which is 5 or above, so round the number up to 0.000194.

Like before, there is no need to add zeros as you have already gone past your decimal point.

So the final answer is 0.000194 to 3 significant figures.

For some more questions on rounding to 3 significant figures click here.

To find the perpendicular gradient from the gradient:

Step A Divide the number into 1 (take the reciprocal)

Step B Change the sign.

If you multiply the gradient of the tangent by the gradient of the normal then this will give you 1.

Alternatively you can use the following formula to find the perpendicular gradient:

Perpendicular gradient = -1/m (m is the gradient of the tangent)

Example 1

Work out the perpendicular gradient if the gradient is 12.

Step A The reciprocal of 12 is 1/12

Step B Changing the sign of 1/12 gives -1/12.

So the perpendicular gradient is -1/12

Example 2

Work out the perpendicular gradient if the gradient is -2.

Step A The reciprocal of -2 is -1/2

Step B Changing the sign of -1/2 gives ½

So the perpendicular gradient is 1/2

Example 3

Work out the perpendicular gradient if the gradient is 3/7.

Step A The reciprocal of 3/7 is 7/3

Step B Changing the sign of 7/3 gives -7/3

So the perpendicular gradient is -7/3

Example 4

Work out the perpendicular gradient if the gradient is -3/4.

Step A The reciprocal of -3/4 is -4/3

Step B Changing the sign of -4/3 gives 4/3

So the perpendicular gradient is 4/3

Example 5

The equation of a straight line is y = 3x + 5. Find an equation of a line that is perpendicular to this line.

First you need to find the perpendicular gradient.

The gradient of the line given is 3 (the number before x)

Step A The reciprocal of 3 is 1/3

Step B Changing the sign of 1/3 gives -1/3

Now the question asks you to find the equation of any line that is perpendicular to y = 3x + 5 so it doesn’t matter what value you choose for the intercept of the perpendicular line.

So you could have y = -1/3x         (intercept is 0).

Thank you to all the people I know whose math classes do not require such pastimes! More videos/info: vihart.com Doodling Snakes + Graphs: ttp://www.youtube.com/watch?v=heKK95DAKms Doodling Stars: www.youtube.com vihart.com

To factorize an expression into a single bracket follow these steps:

a) First find the greatest common divisor of the numbers in your expression. This is the highest number that your numbers in your expression can be divided by without giving a remainder. Put the greatest common divisor outside the bracket.

b) Also put other letters outside your bracket that are common to all terms in the expression.

c) Finally, fill the terms inside the bracket to give you the original expression once the bracket is expanded.

Example 1

Factorize 12a + 14ab

Here the Greatest Common Divisor is 2, and there is an a in both terms of the expression. Put these outside the bracket.

2a(? + ?)

Now, 2a multiplied by 6 gives 12a and 2a multiplied by 7b gives 14ab.

So your final answer is:

2a(6 + 7b)

Example 2

Factorize 15xy – 9y.

Here the Greatest Common Divisor is 3, and there is a y in both terms of the expression. Put these outside the bracket.

3y(? – ?)

Now 3y multiplied by 5x gives 15xy and 3y multiplied by 3 gives 9y

So your final answer is:

3y(5x – 3)

Example 3

Factorize 16x²y + 12xy

Here the Greatest Common Divisor is 4, and there is a x and y in both terms of the expression. Put these outside the bracket:

4xy(? + ?)

Now 4xy multiplied by 4x gives 16x²y and 4xy multiplied by 3 gives 12xy.

So your final answer is:

4xy(4y + 3)

For some more examples on factorizing expressions into single brackets click here.

For some harder questions on factorizing expressions with 3 terms click here.

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Counting is an essential part of learning for kids. However it is necessary to make counting for kids interesting so that they like it instead of getting bored. It is an activity that enhances numerical expertise from a very early age. Later on it helps them to tackle complex mathematical problems with ease. There are lots of educational toys meant for children which are designed to hone their different skills. These toys make learning fun and exciting. To help improve counting abilities of children there are math toys which are available in different varieties. Visual and moving elements are incorporated into these toys to make them realistic. Your child will love these toys.

It is imperative that you provide your child a conductive learning environment. Learning requires stimulation and this must be done from a very tender age. Thankfully nowadays you have so many educational toys that can help in the learning process. The beginning part can be difficult for you like choosing the right toy. However you can make this easy by choosing a simple toy and as your child progresses you can bring in complex toys. When you buy math toys (matematik legetøj) for your child keep in mind your child’s interest. Get something which your child would love to play with.

Mathematical learning toys for children should be such that it helps your child become familiar with numbers. Encourage your child to play with the toys and if necessary participate with your child. Gradually as your child progresses bring in toys with maths concepts. Your child will learn basic concepts of arithmetic like addition, sorting, counting etc. When you buy toys always keep in mind your child’s level of ability and the quality of the toy.

There are other learning toys (lærende legetøj) too which help children to understand their daily lessons better. Starting from little toys meant for infants there are different types of toys that cater to children up to their teenage years. Some toys are so challenging that even parents get stumped sometimes. Toys not only entertain kids, but also stimulate their minds. This aids in their development.

If your child has a penchant for music, give him or her toys that play classical music. This will help enhance the imagination of your child. For kindergarten children interactive toys are highly recommended. These help them learn words as well as numbers. There are so many educational toys and each comes with a purpose. Children love toys, so give them toys that make them enjoy as well as learn.

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Related Math Articles

Maths GCSE is a very important qualification to hold, in most parts of the United Kingdom. Many adults both young and old for whatever reason may not have passed their GCSE maths first time, or may not have even had the chance to take it. Starting a course from scratch can be daunting however, it can help towards moving on to further educational courses which could eventually lead to higher education at degree level or an alternative to degree level study.

Distance learning is an option that has become very popular in recent years, giving those who may not have the time to study a full time classroom based course the option to gain the qualifications they need from the comfort of their own home. Distance learning maths courses can also be used for gaining entry to teacher training courses such as the Postgraduate Certificate in Education better known as the PGCE. The majority of maths home learning courses are approved by and suitable for the main examining boards such as Edexcel and AQA.

Home learning is suited to individuals such as single mothers who cannot find the time to go into college to study. Even people who are working and want to gain extra qualifications to improve their career prospects. There are more and more options for individuals who want to change their lives for the better without sacrificing work or family life.

The majority of home learning maths courses can be completed in the students own time and are usually entirely flexible. The only time the student would have to go into college or an educational institution would be to take the formal exams. These usually take place at a local college or educational centre. It is up to the student to contact the establishment and make arrangements to sit the exams. All students studying a home learning course will have to make the institution aware that they are entering as a private candidate; therefore they will be responsible for paying the examination fee.

The cost of a maths home study course is affordable, therefore giving anyone who wants to take up study the option to do so without the worry of excessive course fees. Most home learning courses are available to purchase easily online, and normally give the student the option to have e mail or phone contact with the course tutor. Therefore although studying will be different from the traditional classroom study, the student is never alone because they always have the option of making contact with the course tutor.

When thinking about studying a home learning maths course it is always a good idea to contact the company to discuss your options before committing to anything. However it is never too late to gain the qualifications one needs to improve their quality of life.

There is debate over whether mathematical objects such as numbers and points exist naturally or are human creations. Most of the mathematical concepts we encounter every day – numbers, addition, subtraction – seem so basic, so hard to avoid in discussing reality on even the most basic level, that it’s hard to imagine someone having to sit down and invent them. Who was the first person to look at two rocks and think, “Two more and I’ve got four?” The very idea almost seems absurd.

But mathematics is, in part, a language – not just a set of logical relationships and entailments that seems deeper than words, but a set of notations that allow us to discover those relationships. You can’t see that twice two makes four, until you have a symbol for “two” that your brain can operate with. And those symbols – that language – did have to develop, strange as it may seem.

If you want to help your kid in hes home work, then the following steps might help you.

Parents look at the big picture. They see the results of missing assignments or poorly done homework on the student’s final grade. They themselves have gone through this in their school years and know of the consequences of bad homework habits. But rarely do parents have a grasp of what to do to change the situation.

First thing is organize and set-up a student study area at home. This could be in their bedroom or the spare room down the hall. Make sure it has a comfortable desk and chair. Put a bulletin board on the wall to pin up note cards and reminders. A calendar is easy to use and convenient to post due dates for important assignments. Buy a good lamp so the area is well lit. Next make sure your child has a book shelve complete with standard reference books such as a dictionary, thesaurus or book of quotes.

Usually parents find their kids need help with their homework when they get a report card or a note from the teacher. Bad grades are indicative of poor homework or missed assignments. Before you blow a gasket- communicate. Find out if they have a process to keep up with assignments and due dates. In a lot of cases this can be the sole reason for their poor grade and is easily communicated and changed if done without anger and fear.

Teach your kids to list their assignments and due dates on a calendar or agenda. Being organized is a big key to success with homework. Maybe they need a date book or calendar to take to school with them so they can transfer important dates, times and assignments to the calendar in the study area?

This is not an easy habit to create over night, by continuing to monitor the students homework and grades parents can get the point across, while ultimately seeing their child do better, because they are keeping organized.

Monitor your child’s progress by utilizing the online grading system or online portal. This is easy and helps you the parent to know what your child is doing in school, what assignments are coming up and how well they did on past assignments. This will enable you to decide if your child needs continual help or maybe an outside tutor.
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