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655-705 (Hard)|   Algebra|   Roots|      
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Bunuel
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What is the Value of (1 + 3^(1/2))(2 + 3^(1/2))^(1/2) 24 Jan 2021, 01:41
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65% (hard)

Question Stats:

64% (02:28) correct 36% (02:36) wrong based on 483 sessions

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What is the Value of \((1+\sqrt{3})(\sqrt{(2+{\sqrt{{3}}})}\) ?


A. \(\sqrt{2}(2-\sqrt{3})\)

B. \(\sqrt{2}(2+\sqrt{2})\)

C. \(\sqrt{2}(2+\sqrt{3})\)

D. \(\sqrt{2}(3+\sqrt{3})\)

E. \(\sqrt{3}(2+\sqrt{3})\)
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GMAT Focus 1: 735 Q90 V89 DI81
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What is the Value of (1 + 3^(1/2))(2 + 3^(1/2))^(1/2) 24 Jan 2021, 02:41
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Bunuel
What is the Value of \((1+\sqrt{3})(\sqrt{(2+{\sqrt{{3}}})}\) ?


A. \(\sqrt{2}(2-\sqrt{3})\)

B. \(\sqrt{2}(2+\sqrt{2})\)

C. \(\sqrt{2}(2+\sqrt{3})\)

D. \(\sqrt{2}(3+\sqrt{3})\)

E. \(\sqrt{3}(2+\sqrt{3})\)
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Let \(x=(1+\sqrt{3})(\sqrt{(2+{\sqrt{{3}}})}\)
\(x^2=(1+\sqrt{3})^2*(\sqrt{(2+{\sqrt{{3}}})}^2=(1+3+2\sqrt{3})(2+\sqrt{3})=2(2+\sqrt{3})(2+\sqrt{3})=2*(2+\sqrt{3})^2\)
\(x=\sqrt{2}(2+\sqrt{3})\)

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What is the Value of (1 + 3^(1/2))(2 + 3^(1/2))^(1/2) 01 Jul 2021, 11:43
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Hi, I am having trouble with most Math Revolution questions. I am not able to develop that mindset needed to solve these logical questions. Any idea on how I should proceed ?
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What is the Value of (1 + 3^(1/2))(2 + 3^(1/2))^(1/2) 02 Jul 2021, 08:08
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Pranjal3107
Hi, I am having trouble with most Math Revolution questions. I am not able to develop that mindset needed to solve these logical questions. Any idea on how I should proceed ?
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Hello,

First of all please make sure where do you post your concern. This question has nothing to do with Math Revolution questions.

If you are finding trouble in solving questions specifically then ask questions or post questions.

Thanks
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What is the Value of (1 + 3^(1/2))(2 + 3^(1/2))^(1/2) 05 Feb 2026, 10:59
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One quick way to tackle this question would be to approxmiate values of roots

Take √3 as 1.7 and √2 as 1.4

So the question becomes
2.7 x √(2+1.7) i.e 2.7 x √3.7

Since 3.7 is slightly less than 4, √3.7 will be slightly less than 2

2.7 x 2 = ~5.4 i.e slightly less than 5.4 i.e 5.1 or 5.2

If you test answer choices
A is 1.4 (0.7) way less than 5.2
B = 1.4 (2+1.4) i.e 1.4 x 3.4 less than 5.2
C = 1.4 (2+1.7) = 1.4 x 3.7 ~ 5.1 answer
D = 1.4 (4.7) ---> more than 5.2
E = 1.7 (2+1.7) i.e 1.7 x 3.7 again more than 5.2
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What is the Value of (1 + 3^(1/2))(2 + 3^(1/2))^(1/2) 20 Feb 2026, 09:50
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Take approximations along the way, for example take root 3 to be 1.7 and root 2 to be 1.4 in this case and just substitute value. Check options for the closest and you will get C in less than a minute.

Good luck!
Pranjal3107
Hi, I am having trouble with most Math Revolution questions. I am not able to develop that mindset needed to solve these logical questions. Any idea on how I should proceed ?
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