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![What is the value of [m][fraction]1/2[/fraction][square_root]√21+12√3[](/forum/styles/gmatclub_light/imageset/icon_post_target_unread.svg "What is the value of [m][fraction]1/2[/fraction][square_root]√21+12√3["){kind=icon}
29 May 2020, 10:20
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Difficulty:
65%
(hard)
Question Stats:
64% (02:19) correct
36%
(02:35)
wrong
based on 396
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What is the value of \(\frac{1}{2}\sqrt{21+12√3}-√3\) ?
(A) \(\frac{1}{2}\)
(B) \(\frac{2}{3}\)
(C) \(\frac{3}{2}\)
(D) \(\frac{6}{7}\)
(E) \(\frac{7}{4}\)
(A) \(\frac{1}{2}\)
(B) \(\frac{2}{3}\)
(C) \(\frac{3}{2}\)
(D) \(\frac{6}{7}\)
(E) \(\frac{7}{4}\)
29 May 2020, 12:16
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\(\frac{1}{2}\sqrt{21+12√3}-√3\)
\(\frac{1}{2}\sqrt{12+9+2√(12*9)}-√3\)
\(\frac{1}{2}\sqrt{(√12+√9)^2} - √3\)
\(\frac{1}{2} [2√3 + 3] -√3\)
\(= \frac{3}{2}\)
\(\frac{1}{2}\sqrt{12+9+2√(12*9)}-√3\)
\(\frac{1}{2}\sqrt{(√12+√9)^2} - √3\)
\(\frac{1}{2} [2√3 + 3] -√3\)
\(= \frac{3}{2}\)
Ravixxx
10 Feb 2022, 22:32
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Ravixxx
Easy way:
\(=\frac{1}{2}\sqrt{21+12√3}-√3\)
\(=\frac{1}{2}\sqrt{9+12√3+12}-√3\)
\(=\frac{1}{2}\sqrt{(3)^2+2*3*2√3+(2√3)^2}-√3\)
\(=\frac{1}{2} \sqrt{(3+2√3)^2}-√3\)
\(=\frac{1}{2} (3+2√3)-√3\)
\(=\frac{(3+2√3-2√3)}{2}\)
\(=\frac{3}{2}\)
