GMAT Question of the Day - Daily to your Mailbox; hard ones only

 It is currently 26 Aug 2019, 00:23

GMAT Club Daily Prep

Thank you for using the timer - this advanced tool can estimate your performance and suggest more practice questions. We have subscribed you to Daily Prep Questions via email.

Customized
for You

we will pick new questions that match your level based on your Timer History

Track

every week, we’ll send you an estimated GMAT score based on your performance

Practice
Pays

we will pick new questions that match your level based on your Timer History

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

Author Message
TAGS:

Hide Tags

VP
Joined: 03 Jun 2019
Posts: 1115
Location: India
What is the the value of (8+3[square_root]21[/square_root])^{[fraction  [#permalink]

Show Tags

10 Aug 2019, 23:32
4
00:00

Difficulty:

55% (hard)

Question Stats:

40% (01:24) correct 60% (01:56) wrong based on 25 sessions

HideShow timer Statistics

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

_________________
"Success is not final; failure is not fatal: It is the courage to continue that counts."

Please provide kudos if you like my post. Kudos encourage active discussions.

My GMAT Resources: -

Efficient Learning

Tele: +91-11-40396815
Mobile : +91-9910661622
E-mail : kinshook.chaturvedi@gmail.com
Manager
Joined: 23 Apr 2018
Posts: 114
Re: What is the the value of (8+3[square_root]21[/square_root])^{[fraction  [#permalink]

Show Tags

10 Aug 2019, 23:43
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

Posted from my mobile device
Director
Joined: 19 Oct 2018
Posts: 791
Location: India
What is the the value of (8+3[square_root]21[/square_root])^{[fraction  [#permalink]

Show Tags

11 Aug 2019, 02:36
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: 114
Re: What is the the value of (8+3[square_root]21[/square_root])^{[fraction  [#permalink]

Show Tags

12 Aug 2019, 03:45
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, 03:45
Display posts from previous: Sort by