# How do you simplify 2(sqrt (7/3)) - (sqrt (3/7)) - 2(sqrt 84)?

Jul 22, 2016

$- 73 \sqrt{\frac{1}{21}}$

#### Explanation:

Any number can be multiplied by 1 without changing its value.

1 can be written in other ways: $\frac{7}{7} = 1 , \frac{3}{3} = 1 , \frac{21}{21} = 1$ etc

Let's try to get the same denominators in the radicals using 1.

Note that $84 = 4 \times 3 \times 7 = 4 \times 21$

$2 \left(\sqrt{\frac{7}{3} \times \frac{7}{7}}\right) - \left(\sqrt{\frac{3}{7} \times \frac{3}{3}}\right) - 2 \left(\frac{\sqrt{4 \times 21 \times 21}}{21}\right)$

=$2 \times 7 \sqrt{\frac{1}{21}} - 3 \sqrt{\frac{1}{21}} - 2 \times 2 \times 21 \sqrt{\frac{1}{21}}$

=$14 \sqrt{\frac{1}{21}} - 3 \sqrt{\frac{1}{21}} - 84 \sqrt{\frac{1}{21}}$

=$- 73 \sqrt{\frac{1}{21}}$