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(1+√3)(√(2 + √3) = ?

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(1+√3)(√(2 + √3) = ? [#permalink]

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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. \(\sqrt{2}(2+\sqrt{2})\)
[Reveal] Spoiler: OA

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Re: (1+√3)(√(2 + √3) = ? [#permalink]

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New post 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

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(1+√3)(√(2 + √3) = ? [#permalink]

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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;

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

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

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

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

\(x = \sqrt{2(2+√3)^2}\)

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

Answer (A)...


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Re: (1+√3)(√(2 + √3) = ? [#permalink]

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New post 27 Sep 2017, 03:00
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√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

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Re: (1+√3)(√(2 + √3) = ?   [#permalink] 27 Sep 2017, 03:00
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