Question

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

Answer 1

`-73sqrt(1/21)`

Explanation:

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)`