# How do you simplify sqrt27+sqrt48?

Jun 9, 2018

$7 \sqrt{3}$

#### Explanation:

Writing
$\sqrt{3 \cdot 9} + \sqrt{3 \cdot 16}$
and usting that
$\sqrt{a b} = \sqrt{a} \cdot \sqrt{b}$ for $a , b \ge 0$
we get
$3 \sqrt{3} + 4 \cdot \sqrt{3} = 7 \sqrt{3}$

Jun 9, 2018

$7 \sqrt{3}$

#### Explanation:

Neither $27$ nor $48$ are perfect squares, but they have factors which are squares.

Find the roots of the factors where possible and then give the answer in surd form.

$\sqrt{27} + \sqrt{48}$

$= \sqrt{\textcolor{b l u e}{9} \times 3} + \sqrt{\textcolor{b l u e}{16} \times 3}$

$= \textcolor{b l u e}{3} \sqrt{3} + \textcolor{b l u e}{4} \sqrt{3}$

$= 7 \sqrt{3} \text{ } \leftarrow$ add like terms