# How do you simplify 6sqrt54?

May 27, 2017

$= 18 \sqrt{6}$

#### Explanation:

the first step when working with roots is to find the factors of the radicand. ($54$), using squares if possible.

$6 \sqrt{54} = 6 \sqrt{9 \times 6} \text{ } \leftarrow$ find the roots if possible.

$6 \sqrt{9 \times 6} \text{ } \leftarrow \left(\sqrt{9} = 3\right)$

$= 6 \times 3 \sqrt{6}$

$= 18 \sqrt{6}$

May 27, 2017

color(brown)(18sqrt6

#### Explanation:

$6 \sqrt{54}$

$\therefore = 6 \sqrt{3 \cdot 3 \cdot 3 \cdot 2}$

$\therefore \sqrt{3} \times \sqrt{3} = 3$

$\therefore = 6 \sqrt{\underline{3 \cdot 3} \cdot 3 \cdot 2}$

$\therefore = 6 \times 3 \sqrt{6}$

:.color(brown)(=18sqrt6