# How do you simplify 7sqrt3*2sqrt6?

May 7, 2017

$42 \sqrt{2}$

#### Explanation:

$\text{using "color(blue)"law of radicals}$

$\textcolor{red}{\overline{\underline{| \textcolor{w h i t e}{\frac{2}{2}} \textcolor{b l a c k}{\sqrt{a} \times \sqrt{b} \Leftrightarrow \sqrt{a \times b}} \textcolor{w h i t e}{\frac{2}{2}} |}}}$

$\Rightarrow 7 \sqrt{3} \times 2 \sqrt{6}$

$= 7 \times 2 \times \sqrt{3} \times \sqrt{6}$

$= 14 \times \sqrt{3 \times 6}$

$= 14 \times \sqrt{18}$

$\left[\text{now } \sqrt{18} = \sqrt{9 \times 2} = \sqrt{9} \times \sqrt{2} = 3 \sqrt{2}\right]$

$= 14 \times 3 \sqrt{2}$

$= 42 \sqrt{2}$

May 7, 2017

See a solution process below:

#### Explanation:

First, we can rewrite this expression as:

$\left(7 \cdot 2\right) \left(\sqrt{3} \cdot \sqrt{6}\right) \to 14 \left(\sqrt{3} \cdot \sqrt{6}\right)$

We can now use this rule for multiplying radicals to continue the simplification:

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

14(sqrt(3) * sqrt(6) => 14 sqrt(3 * 6) => 14sqrt(18)

We can now use the same rule we used above but in reverse to rewrite this expression as:

$14 \sqrt{18} \implies 4 \sqrt{9 \cdot 2} \implies 4 \left(\sqrt{9} \cdot \sqrt{2}\right) \implies 14 \left(\pm 3 \cdot \sqrt{2}\right) \implies$

$\pm 42 \sqrt{2}$

May 7, 2017

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

so, $\sqrt{6} = \sqrt{3.} \sqrt{2}$

Then, $7 \sqrt{3.} \left(2 \sqrt{6}\right) = 7 \sqrt{3.} \left(2 \sqrt{3}\right) . \sqrt{2}$

i.e. $14 \left(3\right) . \sqrt{2}$

so, $42 \sqrt{2}$

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