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What is the the value of (8+3[square_root]21[/square_root])^{[fraction

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What is the the value of (8+3[square_root]21[/square_root])^{[fraction  [#permalink]

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New post 10 Aug 2019, 22:32
6
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A
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Difficulty:

  55% (hard)

Question Stats:

39% (01:21) correct 61% (01:54) wrong based on 33 sessions

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What is the the value of \((8+3\sqrt{21})^{\frac{1}{3}}+ (8-3\sqrt{21})^{\frac{1}{3}}?\)

A. 0
B. 1
C. 2
D. 4
E. 8

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What is the the value of (8+3[square_root]21[/square_root])^{[fraction  [#permalink]

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New post 11 Aug 2019, 01:36
1
x= \((8+3\sqrt{21})^{\frac{1}{3}}+ (8-3\sqrt{21})^{\frac{1}{3}}\)

\((a+b)^3= a^3+b^3+3*a*b*(a+b)\)

\(x^3\)= \((8+3\sqrt{21})\)+\((8-3\sqrt{21})\)+\(3*[8+3\sqrt{21}]^{1/3}\)*\([8-3\sqrt{21}]^{1/3} x\)

\(x^3= 16-15x\)

x=1

B

Kinshook wrote:
What is the the value of \((8+3\sqrt{21})^{\frac{1}{3}}+ (8-3\sqrt{21})^{\frac{1}{3}}?\)

A. 0
B. 1
C. 2
D. 4
E. 8
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Re: What is the the value of (8+3[square_root]21[/square_root])^{[fraction  [#permalink]

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New post 10 Aug 2019, 22:43
1
Opening the brackets
8^1/3 = 2
3 sqroot21 ^1/3 = 21^1/9
We get
2+21^1/9+2-21^1/9
Cancel 21^1/9 with each other
2+2
=4 option D

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Re: What is the the value of (8+3[square_root]21[/square_root])^{[fraction  [#permalink]

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New post 12 Aug 2019, 02:45
nick1816 wrote:
x= \((8+3\sqrt{21})^{\frac{1}{3}}+ (8-3\sqrt{21})^{\frac{1}{3}}\)

\((a+b)^3= a^3+b^3+3*a*b*(a+b)\)

\(x^3\)= \((8+3\sqrt{21})\)+\((8-3\sqrt{21})\)+\(3*[8+3\sqrt{21}]^{1/3}\)*\([8-3\sqrt{21}]^{1/3} x\)

\(x^3= 16-15x\)

x=1

B

Kinshook wrote:
What is the the value of \((8+3\sqrt{21})^{\frac{1}{3}}+ (8-3\sqrt{21})^{\frac{1}{3}}?\)

A. 0
B. 1
C. 2
D. 4
E. 8




can you elaborate on how to solve the highlighted part ?
GMAT Club Bot
Re: What is the the value of (8+3[square_root]21[/square_root])^{[fraction   [#permalink] 12 Aug 2019, 02:45

What is the the value of (8+3[square_root]21[/square_root])^{[fraction

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