How do you solve 2 sqrt 12 + 4 sqrt 27?

May 17, 2018

$2 \sqrt{12} + 4 \sqrt{27} = 16 \sqrt{3}$

Explanation:

show below

$2 \sqrt{12} + 4 \sqrt{27} = 2 \sqrt{4 \cdot 3} + 4 \sqrt{9 \cdot 3}$

$2 \cdot \sqrt{4} \cdot \sqrt{3} + 4 \cdot \sqrt{9} \cdot \sqrt{3} = 2 \cdot 2 \cdot \sqrt{3} + 4 \cdot 3 \cdot \sqrt{3}$

$4 \sqrt{3} + 12 \sqrt{3} = 16 \sqrt{3}$

May 17, 2018

See a solution process below:

Explanation:

First, rewrite the terms under the radicals as:

$2 \sqrt{4 \cdot 3} + 4 \sqrt{9 \cdot 3} \implies$

$2 \sqrt{4} \sqrt{3} + 4 \sqrt{9} \sqrt{3} \implies$

$\left(2 \cdot 2\right) \sqrt{3} + \left(4 \cdot 3\right) \sqrt{3} \implies$

$4 \sqrt{3} + 12 \sqrt{3}$

Now, we can factor out the common term giving:

$\left(4 + 12\right) \sqrt{3} \implies$

$16 \sqrt{3}$