# How do you simplify 3 times the square root of 20 + 2 times the square root of 45?

Mar 10, 2018

$12 \sqrt{5}$

#### Explanation:

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

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$\Rightarrow 3 \sqrt{20} + 2 \sqrt{45}$

$= \left(3 \times \sqrt{4 \times 5}\right) + \left(2 \times \sqrt{9 \times 5}\right)$

$= \left(3 \times \sqrt{4} \times \sqrt{5}\right) + \left(2 \times \sqrt{9} \times \sqrt{5}\right)$

$= \left(3 \times 2 \times \sqrt{5}\right) + \left(2 \times 3 \times \sqrt{5}\right)$

$= 6 \sqrt{5} + 6 \sqrt{5}$

$= 12 \sqrt{5}$

Mar 10, 2018

$12 \sqrt{5}$

#### Explanation:

$\sqrt{20} = 2 \sqrt{5}$
$3 \cdot 2 \sqrt{5}$
$6 \sqrt{5}$

$\sqrt{45} = 3 \sqrt{5}$
$2 \cdot 3 \sqrt{5} = 6 \sqrt{5}$

$6 \sqrt{5} + 6 \sqrt{5} = 12 \sqrt{5}$