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

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CEO
Joined: 03 Jun 2019
Posts: 3338
Location: India
GMAT 1: 690 Q50 V34
WE: Engineering (Transportation)
What is the the value of (8+3[square_root]21[/square_root])^{[fraction  [#permalink]

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10 Aug 2019, 22:32
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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

_________________
Kinshook Chaturvedi
Email: kinshook.chaturvedi@gmail.com
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Joined: 23 Apr 2018
Posts: 160
Re: What is the the value of (8+3[square_root]21[/square_root])^{[fraction  [#permalink]

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

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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
Manager
Joined: 23 Apr 2018
Posts: 160
Re: What is the the value of (8+3[square_root]21[/square_root])^{[fraction  [#permalink]

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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 ?
Re: What is the the value of (8+3[square_root]21[/square_root])^{[fraction   [#permalink] 12 Aug 2019, 02:45