# How do you solve 3(sqrt12)+4(sqrt18)?

May 13, 2017

See a solution process below:

#### Explanation:

First, use this rule of radicals to rewrite the expression:

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

$3 \left(\sqrt{12}\right) + 4 \left(\sqrt{18}\right) \implies$

$3 \left(\sqrt{4 \cdot 3}\right) + 4 \left(\sqrt{9 \cdot 3}\right) \implies$

$3 \left(\sqrt{4} \cdot \sqrt{3}\right) + 4 \left(\sqrt{9} \cdot \sqrt{3}\right) \implies$

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

$6 \sqrt{3} + 12 \sqrt{3}$

We can now factor a $\sqrt{3}$ out of each term and calculate the result:

$6 \sqrt{3} + 12 \sqrt{3} \implies$

$\left(6 + 12\right) \sqrt{3} \implies$

$18 \sqrt{3}$

Or

$31.177$ rounded to the nearest thousandth.