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# (1+√3)(√(2 + √3) = ?

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Intern
Joined: 31 Mar 2017
Posts: 37
GMAT 1: 710 Q45 V42
GMAT 2: 730 Q50 V39
GPA: 3.73
(1+√3)(√(2 + √3) = ? [#permalink]

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13 Aug 2017, 14:00
1
6
00:00

Difficulty:

55% (hard)

Question Stats:

64% (01:57) correct 36% (02:11) wrong based on 109 sessions

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$$(1+\sqrt{3}) \sqrt{(2+√3)}$$ = ?

A. $$\sqrt{2}(2+\sqrt{3})$$
B. $$\sqrt{2}(3+\sqrt{3})$$
C. $$\sqrt{2}(2-\sqrt{3})$$
D. $$\sqrt{3}(2+\sqrt{3})$$
E. $$\sqrt{2}(2+\sqrt{2})$$
Manager
Joined: 26 Jun 2017
Posts: 243
Location: Russian Federation
Concentration: General Management, Strategy
WE: Information Technology (Other)
Re: (1+√3)(√(2 + √3) = ? [#permalink]

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13 Aug 2017, 14:40
jwang516 wrote:
$$(1+\sqrt{3}) \sqrt{(2+√3)}$$ = ?

A. $$\sqrt{2}(2+\sqrt{3})$$
B. $$\sqrt{2}(3+\sqrt{3})$$
C. $$\sqrt{2}(2-\sqrt{3})$$
D. $$\sqrt{3}(2+\sqrt{3})$$
E. $$\sqrt{2}(2+\sqrt{2})$$

Lets check the square of original expression.
sqr((1+√3)(√(2 + √3))=sqr(1+√3)*sqr(√(2 + √3)=(4+2√3)(2+√3)=2sqr(2+√3).
Now lets take the square root from our square - it will be the original expression.
sqrt(2sqr(2+√3)) = √2((2+√3)) - option A
Director
Joined: 04 Dec 2015
Posts: 700
Location: India
Concentration: Technology, Strategy
Schools: ISB '19, IIMA , IIMB, XLRI
WE: Information Technology (Consulting)
(1+√3)(√(2 + √3) = ? [#permalink]

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13 Aug 2017, 14:54
7
2
jwang516 wrote:
$$(1+\sqrt{3}) \sqrt{(2+√3)}$$ = ?

A. $$\sqrt{2}(2+\sqrt{3})$$
B. $$\sqrt{2}(3+\sqrt{3})$$
C. $$\sqrt{2}(2-\sqrt{3})$$
D. $$\sqrt{3}(2+\sqrt{3})$$
E. $$\sqrt{2}(2+\sqrt{2})$$

Let, $$x = (1+\sqrt{3}) \sqrt{(2+√3)}$$

Let, $$a = (1+\sqrt{3})$$

$$b = (2+\sqrt{3})$$

$$x = a\sqrt{b}$$

Squaring both sides;

$$x^2 = (a\sqrt{b})^2 => (a^2)(b)$$

$$a^2 = (1+\sqrt{3})^2 = 1 + 2\sqrt{3} + 3 = 4 + 2\sqrt{3} => 2(2 + \sqrt{3})$$

$$(a^2)(b) = 2(2 + \sqrt{3})(2+\sqrt{3}) => 2(2+\sqrt{3})^2$$

$$x^2 = (a^2)(b) = 2(2+\sqrt{3})^2$$

$$x = \sqrt{2(2+√3)^2}$$

$$x = \sqrt{2}(2+\sqrt{3})$$

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Manager
Joined: 04 May 2014
Posts: 162
Location: India
WE: Sales (Mutual Funds and Brokerage)
Re: (1+√3)(√(2 + √3) = ? [#permalink]

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27 Sep 2017, 03:00
1
√3=1.7
√2=1.4
(1+√3)(√(2 + √3)=(1+1.7)(√(2 + 1.7)=(2.7)(√3.7) now (√3.7)≈2
The product =2.7X(2+)=5.4
I checked for all the answer choices given but will show here only for the correct one.
A. √2(2+√3)=1.4(2+1.7)=1.4(3.7)=5.18. This is close to 5.4
Re: (1+√3)(√(2 + √3) = ?   [#permalink] 27 Sep 2017, 03:00
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