# How do you solve #x^2 = 256#?

##### 2 Answers

Jan 10, 2016

Jan 10, 2016

This has two solutions

#### Explanation:

One way to look for square roots of numbers is to start by factorising them.

In this example,

#256 = 2 * 128#

Then

#256 = 2 * 2 * 64#

Keep on going until you find:

#256 = 2*2*2*2*2*2*2*2 = 2^8#

At this point it is clear that:

#256 = (2*2*2*2)*(2*2*2*2) = 2^4*2^4 = (2^4)^2 = 16^2#

So

#(-16)^2 = (-16)*(-16) = 256#