# How do you simplify sqrt147+6sqrt3?

Aug 27, 2016

$\sqrt{147} + 6 \sqrt{3} = 13 \sqrt{3}$

#### Explanation:

$\sqrt{147} + 6 \sqrt{3} = \sqrt{{7}^{2} \cdot 3} + 6 \sqrt{3} = \sqrt{{7}^{2}} \sqrt{3} + 6 \sqrt{3} = 7 \sqrt{3} + 6 \sqrt{3} = 13 \sqrt{3}$

In general, when you are asked to simply anything like $\sqrt{147}$ start by factoring the radicand:

$147 = 3 \cdot 7 \cdot 7 = 3 \cdot {7}^{2}$

Since this has a square factor we can simplify its square root as shown above.