# How do you solve x^2 = 256?

Jan 10, 2016

You just take the square root of both sides. Square root of ${x}^{2}$ would give you an x. $\sqrt{256}$ would give you 16.

Jan 10, 2016

This has two solutions $x = 16$ and $x = - 16$

#### Explanation:

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

In this example, $256$ is obviously even, so divide it by $2$ to find:

$256 = 2 \cdot 128$

Then $128$ is even, so divide that by $2$ to find:

$256 = 2 \cdot 2 \cdot 64$

Keep on going until you find:

$256 = 2 \cdot 2 \cdot 2 \cdot 2 \cdot 2 \cdot 2 \cdot 2 \cdot 2 = {2}^{8}$

At this point it is clear that:

$256 = \left(2 \cdot 2 \cdot 2 \cdot 2\right) \cdot \left(2 \cdot 2 \cdot 2 \cdot 2\right) = {2}^{4} \cdot {2}^{4} = {\left({2}^{4}\right)}^{2} = {16}^{2}$

So $16$ is a solution, but $- 16$ is also a solution since:

${\left(- 16\right)}^{2} = \left(- 16\right) \cdot \left(- 16\right) = 256$