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

2 Answers
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

Answer:

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#