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What is the Value of (1 + 3^(1/2))(2 + 3^(1/2))^(1/2)

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Intern
Joined: 04 Feb 2018
Posts: 10
Location: India
What is the Value of (1 + 3^(1/2))(2 + 3^(1/2))^(1/2)  [#permalink]

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Updated on: 02 Oct 2018, 01:10
1
3
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Difficulty:

65% (hard)

Question Stats:

59% (02:11) correct 41% (02:35) wrong based on 56 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.$$\sqrt{3}(2+\sqrt{3})$$

Originally posted by rheabiswal on 02 Oct 2018, 01:07.
Last edited by Bunuel on 02 Oct 2018, 01:10, edited 1 time in total.
Renamed the topic and edited the question.
Math Expert
Joined: 02 Aug 2009
Posts: 7334
What is the Value of (1 + 3^(1/2))(2 + 3^(1/2))^(1/2)  [#permalink]

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02 Oct 2018, 02:49
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rheabiswal wrote:
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.$$\sqrt{3}(2+\sqrt{3})$$

$$(1+\sqrt{3})(\sqrt{(2+{\sqrt{{3}}})}$$ =$$\sqrt{(1+\sqrt{3})^2(2+\sqrt{3})}=\sqrt{(1+3+2\sqrt{3})(2+\sqrt{3})}=\sqrt{2(2+√3)(2+√3)}=\sqrt{2}(2+\sqrt{3})$$

C
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1) Absolute modulus : http://gmatclub.com/forum/absolute-modulus-a-better-understanding-210849.html#p1622372
2)Combination of similar and dissimilar things : http://gmatclub.com/forum/topic215915.html
3) effects of arithmetic operations : https://gmatclub.com/forum/effects-of-arithmetic-operations-on-fractions-269413.html
4) Base while finding % increase and % decrease : https://gmatclub.com/forum/percentage-increase-decrease-what-should-be-the-denominator-287528.html

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What is the Value of (1 + 3^(1/2))(2 + 3^(1/2))^(1/2)   [#permalink] 02 Oct 2018, 02:49
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