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

Question

1836 views around the world

You can reuse this answer
Creative Commons License

Answer 1 · 2016-07-22T12:13:50

$-73sqrt(1/21)$

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

1 can be written in other ways: $7/7 =1, 3/3 =1, 21/21 =1$ etc

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

Note that $84 = 4xx3xx7 = 4 xx 21$

$2(sqrt (7/3 xx7/7)) - (sqrt (3/7 xx3/3)) - 2(sqrt(4xx21xx21)/21)$

= $2xx7sqrt(1/21) -3sqrt(1/21)-2xx2xx21sqrt(1/21)$

= $14sqrt(1/21) -3sqrt(1/21)-84sqrt(1/21)$

= $-73sqrt(1/21)$

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