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A
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Difficulty:
75%
(hard)
Question Stats:
57% (02:12) correct
43%
(02:43)
wrong
based on 156
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\(\sqrt{9 + 4√5} + \sqrt{30 − 10√5} \) =
A) 7
B) \(3 + 2\sqrt{5}\)
C) \(19.5 − 3\sqrt{5}\)
D) \(39 − 6\sqrt{5}\)
E) \(140 − 60\sqrt{5}\)
A) 7
B) \(3 + 2\sqrt{5}\)
C) \(19.5 − 3\sqrt{5}\)
D) \(39 − 6\sqrt{5}\)
E) \(140 − 60\sqrt{5}\)
29 Jun 2021, 06:53
Kudos
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sjuniv32
Approximate value
\(\sqrt{5}=2.2\)
\(\sqrt{9 + 4√5} + \sqrt{30 − 10√5} \)
\(\sqrt{9 + 4*2.2} + \sqrt{30 − 10*2.2} \)
\(\sqrt{17.8} + \sqrt{7.8} \)
This is surely greater than 4+2 or 6 and less than 5+3 or 8.
So A or B. Difficult to choose any one between them visually but probability is 50% now.
Solve the expression
It is a square root so we have to check whether we can make the terms that are under square root as squares.
\(\sqrt{9 + 4√5} + \sqrt{30 − 10√5} \) =x
\(\sqrt{4+ 5+ 2*2*√5} +\sqrt{25+5 − 2*5√5}\)
\(\sqrt{2^2+ √5 ^2+ 2*2*√5} +\sqrt{5^2+ √5^2 − 2*5√5}\)
\(\sqrt{(2+ √5)^2}+\sqrt{(5-√5)^2}\)
\(2+ √5+5-√5\)
\(7\)
A
General Discussion
Oppenheimer1945
Joined: 16 Jul 2019
Last visit: 14 Nov 2025
Posts: 784
Given Kudos: 223
Location: India
Schools: INSEAD '26 (D) ISB '27 (D) IIMB '26 (A) IIMA '26 (A) HEC '26 (D) LBS '26 IESE '27 (D) Fuqua '27 (WL) Tepper '27 (WL)
GMAT Focus 1: 645 Q90 V76 DI80 
GPA: 7.81
Schools: INSEAD '26 (D) ISB '27 (D) IIMB '26 (A) IIMA '26 (A) HEC '26 (D) LBS '26 IESE '27 (D) Fuqua '27 (WL) Tepper '27 (WL)
GMAT Focus 1: 645 Q90 V76 DI80
Posts: 784
04 Feb 2024, 01:49
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\(\sqrt{(a^2+b^2+2ab)}=|a+b|\\
\sqrt{(a^2+b^2-2ab)}=|a-b|\\
\\
4\sqrt{5}=2ab\\
=>ab=2\sqrt{5}\\
2^2+(\sqrt{5})^2=9\\
\\
10\sqrt{5}=2ab\\
=>5\sqrt{5}=ab\\
=>5^2+(\sqrt{5})^2=30\\
\\
T1=2+\sqrt{5}\\
\\
T2=(5-\sqrt{5})\)
T1+T2=7
\sqrt{(a^2+b^2-2ab)}=|a-b|\\
\\
4\sqrt{5}=2ab\\
=>ab=2\sqrt{5}\\
2^2+(\sqrt{5})^2=9\\
\\
10\sqrt{5}=2ab\\
=>5\sqrt{5}=ab\\
=>5^2+(\sqrt{5})^2=30\\
\\
T1=2+\sqrt{5}\\
\\
T2=(5-\sqrt{5})\)
T1+T2=7
