# How do you simplify sqrt(216t)+sqrt(96t)?

Dec 26, 2016

$= 10 \sqrt{6 t}$

#### Explanation:

Find the prime factors under each root - then you know what you are working with...

$\sqrt{{2}^{3} \times {3}^{3} \times t} + \sqrt{{2}^{5} \times 3 \times t} \text{ } \leftarrow$ make even indices

$= \sqrt{{2}^{2} \times 2 \times {3}^{2} \times 3 \times t} + \sqrt{{2}^{4} \times 2 \times 3 \times t}$

$= 2 \times 3 \sqrt{2 \times 3 \times t} + {2}^{2} \sqrt{2 \times 3 \times t} \text{ } \leftarrow$ find possible roots

$= 2 \times 3 \sqrt{6 t} + 2 \times 2 \sqrt{6 t} \text{ } \leftarrow$ factor out the HCF

$= 2 \sqrt{6 t} \left(3 + 2\right)$

$= 2 \times 5 \sqrt{6 t}$

$= 10 \sqrt{6 t}$