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

Aug 28, 2016

For any Real value of $x$

$\sqrt{300 {x}^{2}} = 10 \sqrt{3} \left\mid x \right\mid$

If we know that $x \ge 0$ then this simplifies further to:

$10 \sqrt{3} x$

#### 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: $\sqrt{{x}^{2}} = \left\mid x \right\mid$

So we find:

$\sqrt{300 {x}^{2}} = \sqrt{{10}^{2} \cdot 3 \cdot {x}^{2}} = \sqrt{{10}^{2}} \cdot \sqrt{3} \cdot \sqrt{{x}^{2}} = 10 \sqrt{3} \left\mid x \right\mid$

If we know that $x \ge 0$ then $\left\mid x \right\mid = x$ and this simplifies further to $10 \sqrt{3} x$