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

 It is currently 23 Jun 2018, 04:43

### 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

# Events & Promotions

###### Events & Promotions in June
Open Detailed Calendar

# If x^(1/6) = 6, then (x^6)^(1/2) =

 new topic post reply Question banks Downloads My Bookmarks Reviews Important topics
Author Message
TAGS:

### Hide Tags

Math Expert
Joined: 02 Sep 2009
Posts: 46291
If x^(1/6) = 6, then (x^6)^(1/2) = [#permalink]

### Show Tags

15 Jan 2018, 06:07
00:00

Difficulty:

25% (medium)

Question Stats:

69% (00:48) correct 31% (00:48) wrong based on 140 sessions

### HideShow timer Statistics

If $$\sqrt[6]{x}=6$$, then $$\sqrt{x^6} =$$

(A) $$6$$

(B) $$6\sqrt{6}$$

(C) $$6^6$$

(D) $$6^{18}$$

(E) $$6^{36}$$

_________________
PS Forum Moderator
Joined: 25 Feb 2013
Posts: 1142
Location: India
GPA: 3.82
If x^(1/6) = 6, then (x^6)^(1/2) = [#permalink]

### Show Tags

15 Jan 2018, 07:46
Bunuel wrote:
If $$\sqrt[6]{x}=6$$, then $$\sqrt{x^6} =$$

(A) $$6$$

(B) $$6\sqrt{6}$$

(C) $$6^6$$

(D) $$6^{18}$$

(E) $$6^{36}$$

$$\sqrt[6]{x}=6$$, raise both sides to the power $$6$$

$$=>x=6^6$$. again raise both sides to the power $$6$$

$$=>x^6=(6^6)^6=6^{36}=(6^{18})^2$$. Now take square root of both the sides

=>$$\sqrt{x^6}=\sqrt{(6^{18})^2}=6^{18}$$

Option D
Math Expert
Joined: 02 Aug 2009
Posts: 5935
Re: If x^(1/6) = 6, then (x^6)^(1/2) = [#permalink]

### Show Tags

15 Jan 2018, 07:52
Bunuel wrote:
If $$\sqrt[6]{x}=6$$, then $$\sqrt{x^6} =$$

(A) $$6$$

(B) $$6\sqrt{6}$$

(C) $$6^6$$

(D) $$6^{18}$$

(E) $$6^{36}$$

$$\sqrt[6]{x}=6........x=6^6$$
$$\sqrt{x^6} = x^{\frac{6}{2}}=x^3=(6^6)^3=6^{18}$$
D
_________________

Absolute modulus :http://gmatclub.com/forum/absolute-modulus-a-better-understanding-210849.html#p1622372
Combination of similar and dissimilar things : http://gmatclub.com/forum/topic215915.html

GMAT online Tutor

Board of Directors
Status: QA & VA Forum Moderator
Joined: 11 Jun 2011
Posts: 3511
Location: India
GPA: 3.5
WE: Business Development (Commercial Banking)
Re: If x^(1/6) = 6, then (x^6)^(1/2) = [#permalink]

### Show Tags

15 Jan 2018, 09:40
Bunuel wrote:
If $$\sqrt[6]{x}=6$$, then $$\sqrt{x^6} =$$

(A) $$6$$

(B) $$6\sqrt{6}$$

(C) $$6^6$$

(D) $$6^{18}$$

(E) $$6^{36}$$

$$\sqrt[6]{x}=6$$

So, $$x = 6^6$$

And, $$x^6 = 6^{36}$$

Thus, $$\sqrt{x^6} = 6^{18}$$, answer will be (D)
_________________

Thanks and Regards

Abhishek....

PLEASE FOLLOW THE RULES FOR POSTING IN QA AND VA FORUM AND USE SEARCH FUNCTION BEFORE POSTING NEW QUESTIONS

How to use Search Function in GMAT Club | Rules for Posting in QA forum | Writing Mathematical Formulas |Rules for Posting in VA forum | Request Expert's Reply ( VA Forum Only )

VP
Status: It's near - I can see.
Joined: 13 Apr 2013
Posts: 1053
Location: India
Concentration: International Business, Operations
GMAT 1: 480 Q38 V22
GPA: 3.01
WE: Engineering (Consulting)
Re: If x^(1/6) = 6, then (x^6)^(1/2) = [#permalink]

### Show Tags

31 May 2018, 03:04
Bunuel wrote:
If $$\sqrt[6]{x}=6$$, then $$\sqrt{x^6} =$$

(A) $$6$$

(B) $$6\sqrt{6}$$

(C) $$6^6$$

(D) $$6^{18}$$

(E) $$6^{36}$$

$$x^{(1/6)} = 6$$

$$x = 6^6$$

$$\sqrt{6^{36}}$$

$$6^{(18)}$$
_________________

"Success is not as glamorous as people tell you. It's a lot of hours spent in the darkness."

Target Test Prep Representative
Status: Head GMAT Instructor
Affiliations: Target Test Prep
Joined: 04 Mar 2011
Posts: 2570
Re: If x^(1/6) = 6, then (x^6)^(1/2) = [#permalink]

### Show Tags

01 Jun 2018, 11:22
Bunuel wrote:
If $$\sqrt[6]{x}=6$$, then $$\sqrt{x^6} =$$

(A) $$6$$

(B) $$6\sqrt{6}$$

(C) $$6^6$$

(D) $$6^{18}$$

(E) $$6^{36}$$

Raising both sides of the first equation to the 6th power, we have:

x = 6^6

So [(6^6)^6]^1/2 = (6^36)^1/2 = 6^18.

_________________

Jeffery Miller
Head of GMAT Instruction

GMAT Quant Self-Study Course
500+ lessons 3000+ practice problems 800+ HD solutions

Director
Joined: 09 Mar 2016
Posts: 609
If x^(1/6) = 6, then (x^6)^(1/2) = [#permalink]

### Show Tags

03 Jun 2018, 04:21
niks18 wrote:
Bunuel wrote:
If $$\sqrt[6]{x}=6$$, then $$\sqrt{x^6} =$$

(A) $$6$$

(B) $$6\sqrt{6}$$

(C) $$6^6$$

(D) $$6^{18}$$

(E) $$6^{36}$$

$$\sqrt[6]{x}=6$$, raise both sides to the power $$6$$

$$=>x=6^6$$. again raise both sides to the power $$6$$

$$=>x^6=(6^6)^6=6^{36}=(6^{18})^2$$. Now take square root of both the sides

=>$$\sqrt{x^6}=\sqrt{(6^{18})^2}=6^{18}$$

Option D

hi there generis, today is International Exponents Day so happy day may you always have "positive exponents"

can you please explain one thing

for example when we raise both parts to the power of 6

$$=>x=6^6$$ we multiply both sides by power 6

so we get $$x^6=6^{36}$$

now when i need to take a square root, does it mean that i need to multiply both sides by the exponent of $${1/2}$$ , because radical sign means raised to the power of $$\frac{1}{2}$$
for example $$\sqrt{16}$$ is the same as $$16^{\frac{1}{2}}$$

so taking square root from both parts $$x^6=6^{36}$$ means $$x^6^{\frac{1}{2}}=6^{36}^{\frac{1}{2}}$$ which is $$x^3=6^{18}$$ ??

many thanks and happy sunday
SC Moderator
Joined: 22 May 2016
Posts: 1759
If x^(1/6) = 6, then (x^6)^(1/2) = [#permalink]

### Show Tags

03 Jun 2018, 10:23
1
dave13 wrote:
niks18 wrote:
Bunuel wrote:
If $$\sqrt[6]{x}=6$$, then $$\sqrt{x^6} =$$

(A) $$6$$

(B) $$6\sqrt{6}$$

(C) $$6^6$$

(D) $$6^{18}$$

(E) $$6^{36}$$

$$\sqrt[6]{x}=6$$, raise both sides to the power $$6$$

$$=>x=6^6$$. again raise both sides to the power $$6$$

$$=>x^6=(6^6)^6=6^{36}=(6^{18})^2$$. Now take square root of both the sides

=>$$\sqrt{x^6}=\sqrt{(6^{18})^2}=6^{18}$$

Option D

hi there generis, today is International Exponents Day so happy day may you always have "positive exponents"

can you please explain one thing

for example when we raise both parts to the power of 6

$$=>x=6^6$$ we multiply both sides by power 6

so we get $$x^6=6^{36}$$

now when i need to take a square root, does it mean that i need to multiply both sides by the exponent of $$(\frac{1}{2})$$ , because radical sign means raised to the power of $$\frac{1}{2}$$
for example $$\sqrt{16}$$ is the same as $$16^{\frac{1}{2}}$$

so taking square root from both parts $$x^6=6^{36}$$ means $$x^6^{\frac{1}{2}}=(6^{36})^{\frac{1}{2}}$$ which is $$x^3=6^{18}$$ ??

many thanks and happy sunday

Quote:
now when i need to take a square root, does it mean that i need to multiply both sides by the exponent of $${1/2}$$ , because radical sign means raised to the power of $$\frac{1}{2}$$

Hi dave13 , yes, you are correct. "Take the square root" = raise the base to the power of $$\frac{1}{2}$$. Often, the exponents get multiplied, just as you have done.

I think you wonder why your answer looks different. Its substance is NOT different.

These different forms of the expression all mean the same thing:
$$\sqrt{x^6}$$

$$(x^6)^{\frac{1}{2}}$$

$$x^{(6*\frac{1}{2})}$$

$$x^3$$

Last one is the same because: $$x^{(6*\frac{1}{2})}=(x)^{((6*\frac{1}{2})=3)}=x^3$$

The prompt asked about this form of the term: $$\sqrt{x^6}$$. So posters above stayed with that form. That's the only difference. Form.

Form can be tricky. You simplified both sides. The answer requires us to simplify only RHS.

Not having to simplify $$\sqrt{x^6}$$ to $$x^3$$ removed one extra step -- the one you took. But your math is correct.

Just watch the form in the question. We can simplify one side without simplifying the other. Simplifying does not change the value of the term.

(Multiplying one side by 2, e.g., does change the value. In that case we would have to multiply the other side by 2.)

I think I got to the heart of your question. If not, ask it a little more specifically. Hope that helps.

P.S. I like your exponent pun, hokey aspect and all. Made me grin. Your avatar makes perfect sense.
_________________

In the depths of winter, I finally learned
that within me there lay an invincible summer.

If x^(1/6) = 6, then (x^6)^(1/2) =   [#permalink] 03 Jun 2018, 10:23
Display posts from previous: Sort by

# If x^(1/6) = 6, then (x^6)^(1/2) =

 new topic post reply Question banks Downloads My Bookmarks Reviews Important topics

 Powered by phpBB © phpBB Group | Emoji artwork provided by EmojiOne Kindly note that the GMAT® test is a registered trademark of the Graduate Management Admission Council®, and this site has neither been reviewed nor endorsed by GMAC®.