Without a calculator, is there a way to have #sqrt(3)# as a result when calculating this: #(2)sqrt(3/4)# ?

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Answer 1 · 2018-04-07T05:18:57

Yes. See below.

#=> 2sqrt(3/4)#

#=> (2sqrt(3))/sqrt(4)#

#=> (2sqrt(3))/(sqrt(2^(2))#

#=> (cancel(2) sqrt(3)) / cancel(2) color(white)(..)[∵ sqrt(2^2) = 2]#

#=> sqrt(3)#

Answer 2 · 2018-04-07T05:19:51

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We know that the square root of #4# is #2#.

Also, #sqrt(3/4)# can be decomposed as #sqrt(3)/sqrt(4)#.