How do you simplify 2sqrt54+5sqrt24?

Apr 24, 2018

$16 \sqrt{6}$

Explanation:

$2 \sqrt{54} + 5 \sqrt{24}$

$54 = 2 \times {3}^{3}$
$24 = {2}^{3} \times 3$

$2 \sqrt{2 \times {3}^{3}} + 5 \sqrt{{2}^{3} \times 3}$

$2 \sqrt{{3}^{2}} \sqrt{2 \times 3} + 5 \sqrt{{2}^{2}} \sqrt{2 \times 3}$

$\left(2 \times 3\right) \sqrt{2 \times 3} + \left(5 \times 2\right) \sqrt{2 \times 3}$

$6 \sqrt{2 \times 3} + 10 \sqrt{2 \times 3}$

$6 \sqrt{6} + 10 \sqrt{6}$

$\left(6 + 10\right) \sqrt{6}$

$16 \sqrt{6}$

Apr 24, 2018

$= 16 \sqrt{6}$

Explanation:

Write the radicand as a product of its factors, if possible using a square number,

$2 \sqrt{54} + 5 \sqrt{24}$

$= 2 \sqrt{\textcolor{b l u e}{9} \times 6} + 5 \sqrt{\textcolor{red}{4} \times 6}$

$= 2 \times \textcolor{b l u e}{3} \sqrt{6} + 5 \times \textcolor{red}{2} \sqrt{6} \text{ } \leftarrow$ find the roots

$= 6 \sqrt{6} + 10 \sqrt{6} \text{ } \leftarrow$ there are like terms

$= 16 \sqrt{6}$