# How do you simplify sqrt(12/27)*sqrt(1/4)?

May 14, 2017

$\frac{1}{3}$

#### Explanation:

$\sqrt{\frac{12}{27}} \cdot \sqrt{\frac{1}{4}} = \frac{\sqrt{4} \cdot \sqrt{3}}{\sqrt{9} \cdot \sqrt{3} \cdot \sqrt{4}}$
$= \frac{1}{\sqrt{9}}$
$= \frac{1}{3}$

May 14, 2017

See a solution process below:

#### Explanation:

First, we can combine the radicals using this rule:

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

$\sqrt{\frac{12}{27}} \cdot \sqrt{\frac{1}{4}} \implies \sqrt{\frac{12}{27} \cdot \frac{1}{4}}$

We can rewrite the term in the radical and cancel common terms:

$\sqrt{\frac{12}{27} \cdot \frac{1}{4}} \implies \sqrt{\frac{12 \cdot 1}{27 \cdot 4}} \implies \sqrt{\frac{4 \cdot 3}{9 \cdot 3 \cdot 4}} \implies$

$\sqrt{\frac{\textcolor{red}{\cancel{\textcolor{b l a c k}{4}}} \cdot \textcolor{b l u e}{\cancel{\textcolor{b l a c k}{3}}}}{9 \cdot \textcolor{b l u e}{\cancel{\textcolor{b l a c k}{3}}} \cdot \textcolor{red}{\cancel{\textcolor{b l a c k}{4}}}}} \implies \sqrt{\frac{1}{9}} \implies \frac{1}{3}$