# How do you find the square root of 529?

##### 3 Answers

Check for divisibility by a perfect square to simplify. You will find that

#### Explanation:

When we try to simplify a square root, we look for perfect square factors.

Do this by testing perfect squares until you get to a number whose square if greater that

So we test

Test

Obviously

Keep going . . .

Use a mixture of methods to find

#### Explanation:

There are quite a few different ways to find square roots.

Here's a bit of a mish-mash for this particular example...

Given

#5|29#

Next, note that

We can approximate where

Since

Hence a good first approximation for

How about

We can use the Babylonian method to find a better approximation.

Given a positive number

#a_(i+1) = (a_i^2+n)/(2a_i)#

So putting

#a_1 = (a_0^2+n)/(2a_0) = (22^2+529)/(2*22) = (484+529)/44 = 1013/44 = 23.02bar(27)#

That looks suspiciously close to

#23^2 = 529#

Thus

#### Explanation:

Do a really rough estimate first using squares of multiples of

so

Now look at the last digit ...

There are only two numbers whose squares end with a

So the possibilities are

However,

My first guess would therefore be

Multiplying confirms that

Hence