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

1 Answer
Aug 28, 2016

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