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

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Answer 1 · 2016-01-10T02:13:43

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 · 2016-01-10T20:00:15

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

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:

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

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