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.

The two numbers that this mental math trick has in common are 25 and 50 consecutively. To begin all we do is simply take our number, so for this example we will use 47.

For example:

Our number:     47.

We first subtract it by 25.        47 – 25 = 22

The product will be the first two number of our answer.     22XX

We then take our number: 47

We now subtract it from 50.         50 – 47 = 3

We take our product and now square it:     3 x 3 = 9

This will be our final number. So the answer should look like this so far:     22X9

Then we place a zero in front of our final number:     2203

Let’s examine another problem.

Our number:     42.

We take 42 and subtract it by 25.     42 – 25 = 17

This will be the first 2 digits of our number.     17XX

Now we will subtract from 50 our number 42.     50 – 42 = 8

We take our product 8 and square it.     8 x 8 = 64.

This product will be the final 2 digits of our number.     1764.

Simple enough?

What may help you significantly is to memorize your square roots between 2 and 9.

A small table of this will be provided at the end of the article for practice along with other questions for excersize.

Before we move onto the excersizes lets consider one more example in dealing with our numbers over fifty so as to get a full sense of how this trick works.

For example:

Our number 53.

We first subtract this number by 25.     53 – 25 = 28.

So the first 2 digits of our number will be 28.     28XX

Since our number is over 50 instead of subtracting our number from 50 we will subtract 50 from our number.

53 – 50 = 3

We now will square our result.     3 x 3 = 9

The product will be the last digit of our number.     28X9.

Like our first example, if the square of our last number is not greater than 1 digit we simply place a zero in front of it for our result.     2809.

The series of numbers is short for this trick, a little practice and soon calculating in your head will be fun and easy.

Try these excersizes:

58 x 58 =          43 x 43 =          49 x 49 =          56 x 56 =          48 x 48 =          53 x 53 =          59 x 59 =          46 x 46 =

Quick reference for numbers between 2 and 9 squared.

2 = 4     3 = 9     4 = 12     5 = 25     6 = 36     7 = 49     8 = 64     9 = 81

Answer to excersizes in reverse order:

8)2116     7)3481     6)2809     5)2304     4)3136     3)2401     2)1849     1)3364

Be sure to check other articles in the “Mental Math Tricks” series and also excersize sheets.