Question

How do you simplify `sqrt(300x^2)`?

Answer 1

For any Real value of `x`

`sqrt(300x^2) = 10sqrt(3)abs(x)`

If we know that `x >= 0` then this simplifies further to:

`10sqrt(3)x`

Explanation:

Note that for any non-zero value of `x`, `x^2` has two square roots, namely `x` and `-x`.

The expression `sqrt(x^2)` denotes the principal square root, which is the non-negative one.

Hence: `sqrt(x^2) = abs(x)`

So we find:

`sqrt(300x^2) = sqrt(10^2*3*x^2) = sqrt(10^2)*sqrt(3)*sqrt(x^2) = 10sqrt(3)abs(x)`

If we know that `x >= 0` then `abs(x) = x` and this simplifies further to `10sqrt(3)x`