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.

To double a number all you need to do is add the number onto itself. First of all partition the number. For example, if your number is 78 break the number down into tens and unit (70 and 8). Or if your number is 348, then your number can be broken down to 300, 40 and 8. Next double each of these numbers and and find the total of these answers.

Let’s take a look at some examples:

Example 1

Double 37.

First of all partition 37.

37 = 30 + 7.

Now double each of these numbers:

30 → 60 (since 30 + 30 = 60)

7 → 14 (since 7 + 7 = 14)

Now add up these numbers:

60 + 14 = 74

Example 2

Double 83.

First of all partition 83.

83 = 80 + 3.

Now double each of these numbers:

80 → 160 (since 80 + 80 = 160)

3 → 6 (since 3 + 3 = 6)

Now add up these numbers:

160 + 6 = 166

Example 3

Double 185

First of all partition 185.

185 = 100 + 80 + 5

Now double each of these numbers:

100 → 200 (since 100 + 100 = 200)

80 → 160 (since 80 + 80 = 160)

5 → 10 (since 5 + 5 = 10)

Now add up these numbers:

200 + 160 + 10 = 370

Example 4

Double 319

First of all partition 319.

319 = 300 + 10 + 9

Now double each of these numbers:

300 → 600 (since 300 + 300 = 600)

10 → 20 (since 10 + 10 = 20)

9 → 18 (since 9 + 9 = 18)

Now add up these numbers:

600 + 20 + 18 = 638

Example 5

Double 3708

First of all partition 3708.

3708 = 3000 + 700 + 8

Now double each of these numbers:

3000 → 6000 (since 3000 + 3000 = 6000)

700 → 1400 (since 700 + 700 = 1400)

8 → 16 (since 8 + 8 = 16)

Now add up these numbers:

6000 + 1400 + 16 = 7456

Halving can be carried out in a similar way. Make sure you read this article on halving numbers.

Amazing Abacus Math Video

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.

Nth term of number sequence worksheet/homework sheet.

1) Work out the nth term of this number sequence 5,8,11,14,17…

2) Calculate the nth term of this number sequence 10,12,14,16,18…

3) What is the nth term of this linear number sequence 2,6,10,14,18…?

4) Work out the nth term of this number sequence 11,16,21,26,31…

5) Calculate the nth term of this number sequence 15,22,29,36,43…

For these next 5 questions you will need to calculate the nth term, and then use the nth term formula to calculate the required term.

6) Work out the 70th term of this number sequence 10,18,26,34,42…

7) Work out the 50th term of this number sequence 8,17,26,35,44…

Calculate the 30th term of this number sequence 3,9,15,21,27…

9) Work out the 40th term of this number sequence 2,12,22,32,42…

10) Calculate the 90th term of this number sequence 7,13,19,25,31….

Answers.

Score 1 mark for Q1 to Q5. For Q6 to Q10 score 1 mark for the nth term and 1 mark for working out the required term.

1) nth term = 3n + 2

2) nth term = 2n + 8

3) nth term = 4n – 2

4) nth term = 5n + 6

5) nth term = 7n + 8

6) nth term = 8n + 2

70th term = 8 × 70 + 2 = 562

7) nth term = 9n -1

50th term = 9 × 50 – 1 = 449

nth term = 6n – 3

30th term = 6 × 30 = 177

9) nth term = 8n – 6

40th term = 8 × 40 – 6 = 314

10) nth term = 6n + 1

90th term = 6 × 90 + 1 = 541

If you score 13-15 marks award a grade A.

 10-12 marks award a grade B.

 7-9 marks award a grade C.

Less than 7 marks award a grade D.

For some extra help on number sequence try these:

nth term of a linear number sequence 1

nth term of a quadratic number sequence

nth term of linear number sequence 2

Related Math Articles

Even and odd number worksheet.

Remember even numbers end in 0,2,4,6,8 and odd numbers end in 1,3,5,7,9. One mark should be avoided for each correct answer. All numbers must be given to gain full marks.

1. Write down the next 2 odd numbers after 9.

2. Write down the next 2 even numbers after 10.

3. Out of this list of numbers write down all the even numbers:

37,46,20,41,39,58,103

4. Out of this list of numbers write down all the odd numbers:

81,90,35,43,78,46,200

5. Write down all the odd number between 70 and 80.

6. Write down all the even numbers between 45 and 55.

7. Write down all the odd numbers between 126 and 136.

127,129,131,133 and 135.

8. Write down all the even numbers between 193 and 203

194,196,198,200 and 202

9. Write down the next 2 numbers in this number sequence 79,81,83,85,87… Also state if the numbers in the sequence are odd or even.

89 and 91 (odd numbers)

10. Write down the next 2 numbers in this number sequence 1004,1006,1008,1010,1012…Also state if the numbers in the sequence are odd or even.

1014 and 1016 (even numbers)

Answers

Score 1 mark for each correct answer. All answers must be given.

1. 11,13

2. 12,14

3. 46,20 and 58

4. 81,35 and 43

5. 71,73,75,77 and 79

6. 46,48,50,52,54

7. 127,129,131,133 and 135.

8. 194,196,198,200 and 202

9. 89 and 91 (odd numbers)

10. 1014 and 1016 (even numbers)

How well did you do?

9-10 Grade A

7-8 Grade B

5-6 Grade C

Less than 5 grade D.

If you are finding this difficult check out these links:

Odd and even numbers

Find More Math Articles

Even and odd number worksheet.

Remember even numbers end in 0,2,4,6,8 and odd numbers end in 1,3,5,7,9. One mark should be avoided for each correct answer. All numbers must be given to gain full marks.

1. Write down the next 2 odd numbers after 9.

2. Write down the next 2 even numbers after 10.

3. Out of this list of numbers write down all the even numbers:

37,46,20,41,39,58,103

4. Out of this list of numbers write down all the odd numbers:

81,90,35,43,78,46,200

5. Write down all the odd number between 70 and 80.

6. Write down all the even numbers between 45 and 55.

7. Write down all the odd numbers between 126 and 136.

127,129,131,133 and 135.

8. Write down all the even numbers between 193 and 203

194,196,198,200 and 202

9. Write down the next 2 numbers in this number sequence 79,81,83,85,87… Also state if the numbers in the sequence are odd or even.

89 and 91 (odd numbers)

10. Write down the next 2 numbers in this number sequence 1004,1006,1008,1010,1012…Also state if the numbers in the sequence are odd or even.

1014 and 1016 (even numbers)

Answers

Score 1 mark for each correct answer. All answers must be given.

1. 11,13

2. 12,14

3. 46,20 and 58

4. 81,35 and 43

5. 71,73,75,77 and 79

6. 46,48,50,52,54

7. 127,129,131,133 and 135.

8. 194,196,198,200 and 202

9. 89 and 91 (odd numbers)

10. 1014 and 1016 (even numbers)

How well did you do?

9-10 Grade A

7-8 Grade B

5-6 Grade C

Less than 5 grade D.

If you are finding this difficult check out these links:

Odd and even numbers

Find More Math Articles