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

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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)#