Help with a radical question?

Question

2*sqrt*(7/3) - *sqrt*(3/7) -2*sqrt*84

please tell me how to simplify this!! dont just give me the answer, i wanna know HOW

Answer 1

I guess that you are trying to get a single square root that is equivalent to the expression above, then proceed as follows.

First break the fractions

2*sqrt(7)/sqrt(3)-sqrt(3) / sqrt(7)-2*sqrt(84)

try to sum the first two elements, they are fractions and sum then as fractions

(2.sqrt(7)*sqrt(7) - sqrt(3) *sqrt(3)) / (sqrt(7)*sqrt(3)) -2*sqrt(84)

but sqrt(7)*sqrt(7) = 7,

and sqrt(3)*sqrt(3) = 3

then you get

(2*7-3)/(sqrt(7)*sqrt(3)) -2.sqrt(84)

but sqrt(7)*sqrt(3) = sqrt(7*3) = sqrt(21)

then you get

11/sqrt(21)-2*sqrt(84)

again, treat these as the sum of one fraction plus another number

then you get

(11 - 2 * sqrt(84) * sqrt(21)) / sqrt(21)

but sqrt(84)sqrt(21) = sqrt(1764) = 42

then you get

(11-2*42)/sqrt(21) = -73/sqrt(21)

then you don't want to bet that ugly sqrt at the denominator, then you multiply both denominator and numerator by sqrt(21), and you get

-73 * sqrt(21) / (sqrt(21) * sqrt(21))

but sqrt(21)*sqrt(21) = 21

then you get

-73*sqrt(21)/21