Anonymous

# WWhat do you have to do to a number (like 27) to find its square route?

I know how to find basic square routes (like 36, 144, 49, etc)

But I want to know what you have to do to find the square route of harder numbers like 27 or 31.

Please try and explain this to me, I'm only eleven.

:]

Relevance

Okay so find the the easiest denominators to work with like 3 & 9 so then square root 9 giving you two 3's. so the answer would be 3 square root 3.

3 and that little line thing 3.

hope i helped :)

• Anonymous

i assume you know what powers are?

2^2 = 4

2^3 = 8

2^4 = 16

2 * 2 = 4

2 * 2 * 2 = 8

2 * 2 * 2 * 2 = 16

when you take something to a decimal power, you're basically dividing.

16 ^ .25 = 2

8 ^ .33 = 2

4 ^ .5 = 2

see how 2 to the 2nd power(2 ^ 2), aka, 2 squared, is 4? then 4 ^ .5 is how you find the square root, which is 2. the other examples, 2 ^ 3 and 2 ^ 4 are called 2 cubed and 2 fourthed, and the last examples above show how you would find out that 2 is the cube root of 8, and the fourth root of 16.

so, to find the square root of any number, take it to the .5 power. to find the cube root, take it to the .33 power(or, more accurately, the 1/3 power). to find the fourth root, take it to the .25 power.

• Anonymous

On paper you mean? You use trial and error, for example, the sq root of 27 must be between 5 and 6, so you square 5.5 and see if that's it, then if it's between 5 and 5.5 you try 5.25, and if it's between 5.5 and 6 you try 5.75, and then if it's between 5.5 and 5.75 you try 5.63, and so on and so on until you get it roughly correct to 2 or 3 decimal places...

But nowadays you just use a calculator, it can take a good 15 to 20 minutes doing it on paper.

(edit)

using the trial and error method

here's my trial run

5.5 squared = 30.25

5.25 squared = 27.5625

5.2 squared = 27.04 (this is about as close as you need to get on paper)

on calculator (5.1961524227166319)