Question

finding the square root of a number

Answer 1

Please continue....

Answer 2

Remember first that finding the square root of a number is the opposite of finding the exponent of a number.
Let's say we need to find the square root of 320. Well, your main goal is to find the factors of 320, that means the numbers that composed 320, then organize them by perfect squares (ie 16,25,36,81,100, etc)
For example: 320= 2*2*2*2*2*2*5, now organize them by perfect squares (the ones you can not make a perfect square just leave it alone)
320= 4*4*4*5 or
320=16*4*5
Once you have the factors, get the square root of each number separately . In this case you can get the square root of 16=4, the square root 4=2, and the square root of 5, since square root of 5 does not have a perfect square is left the same way .
Now, just multiply your answers 4*2*√5=8√5.

As you can see √320=8√5

If you want to find the approximate value of 8√5, you need to find the value of √5, well think of an easy square root you know, for example √4=2, therefore, √5≅2.2.
Now going back to your problem: 8√5≅8*(2.2)≅ 17.6

You can do this with any number:
For example:
√90 then find a square root close to √90, like √81= 9, so √90 ≅9.4
√27≅5.1 (from √25=5)
√43≅ 6.5 (from √49=7)