# What is sqrt(49n^3)?

May 25, 2017

See a solution process below:

#### Explanation:

First, use this rule for radicals to simplify the constant:

$\sqrt{a \cdot b} = \sqrt{a} \cdot \sqrt{b}$

$\sqrt{49 {n}^{3}} \implies \sqrt{49 \cdot {n}^{3}} = \sqrt{49} \cdot \sqrt{{n}^{3}} \implies$

$7 \sqrt{{n}^{3}}$

Use this same rule to simplify the $n$ term:

$7 \sqrt{{n}^{3}} \implies 7 \sqrt{{n}^{2} \cdot n} \implies 7 \left(\sqrt{{n}^{2}} \cdot \sqrt{n}\right) \implies$

$7 n \sqrt{n}$

May 25, 2017

$7 n \sqrt{n}$

#### Explanation:

$\sqrt{49 {n}^{3}}$ can be rewritten as follows

$\sqrt{49 {n}^{3}} \to \sqrt{\underline{7 \cdot 7} \cdot \underline{n \cdot n} \cdot n}$

See the underlined parts in the square root? This means we can take out the two $\textcolor{red}{7 ' s}$ and the two $\textcolor{red}{n ' s}$ to get

$7 n \sqrt{n}$, which is in its most simplified form