Question

How do you simplify \[{x^2} = 256\]?

Answer 1

Hint: In the given question, we have been asked to calculate the value of the expression. This expression is a variable raised to the power of a number. We have to find the value of the variable when it is raised to power of no number, or the variable is raised to the power of one. To do that we take the \[{n^{th}}\] root of the equation, where \[n\] is the power to which the number is raised and find the answer.

Complete step by step answer:
The given equation is \[{x^2} = 256\], or
\[x = \sqrt {256} \]
So, we have to find the square root of \[256\].
We know, \[256 = {\left( { \pm 16} \right)^2}\]

Hence, \[x = \sqrt {256} = \sqrt {{{\left( { \pm 16} \right)}^2}} = \pm 16\]

Note: In the given question we had to find the square root of a number. We did that by writing the number whose square the given is. Then we wrote that number as well as the negative of that number because a number and its negative have the same square. This is the point where quite a number of students make the mistake as they would write just the positive number and would forget to write the negative one. This could cost some marks. Also, if we do not remember the square root, we could calculate that by following the method of prime factorization and using that to find it.