Question

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

Answer 1

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.

Answer 2

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 * 128`

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

`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` is a solution, but `-16` is also a solution since:

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