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Which of the following is the value of root{3rd rt{0,000064}

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Which of the following is the value of root{3rd rt{0,000064} [#permalink] New post 30 Jul 2012, 01:02
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A
B
C
D
E

Difficulty:

  15% (low)

Question Stats:

74% (01:41) correct 26% (00:36) wrong based on 469 sessions
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Re: Which of the following is the value of root{3rd rt{0,000064} [#permalink] New post 30 Jul 2012, 01:02
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SOLUTION

Which of the following is the value of \sqrt{\sqrt[3]{0.000064}}

(A) 0.004
(B) 0.008
(C) 0.02
(D) 0.04
(E) 0.2

There are many ways to solve this problem, for example:

\sqrt{\sqrt[3]{0.000064}}=\sqrt[6]{0.000064}=\sqrt[6]{\frac{2^6}{10^6}}=\frac{2}{10}=0.2.

Answer: E.

For theory on exponents and roots check:
math-number-theory-88376.html

For practice on exponents and roots check:
tough-and-tricky-exponents-and-roots-questions-125967.html (DS problems)
tough-and-tricky-exponents-and-roots-questions-125956.html (PS problems)

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Re: Which of the following is the value of root{3rd rt{0,000064} [#permalink] New post 30 Jul 2012, 01:39
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(E) .02

For simplicity
0.000064 can be \frac{64}{1000000}

Its cube root would be \frac{\sqrt[3]{64}}{\sqrt[3]{1000,000}}
i.e. \frac{4}{100}

its square root would be \frac{\sqrt[2]{4}}{\sqrt[2]{100}}
i.e. \frac{2}{10}

i.e. 0.2
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Re: Which of the following is the value of root{3rd rt{0,000064} [#permalink] New post 30 Jul 2012, 02:04
E it is...

= [(64/1000000)^1/3]^1/2
= [(4^3/10^6)^1/3]^1/2
= [ 4/10^2]^1/2
= 2/10
=0.2
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Re: Which of the following is the value of root{3rd rt{0,000064} [#permalink] New post 31 Jul 2012, 06:40
Hi,

can you please explain hoe you arrived at

[ 4/10^2]^1/2

Regards
Sanjiv
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Re: Which of the following is the value of root{3rd rt{0,000064} [#permalink] New post 03 Aug 2012, 03:59
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SOLUTION

Which of the following is the value of \sqrt{\sqrt[3]{0.000064}}

(A) 0.004
(B) 0.008
(C) 0.02
(D) 0.04
(E) 0.2

There are many ways to solve this problem, for example:

\sqrt{\sqrt[3]{0.000064}}=\sqrt[6]{0.000064}=\sqrt[6]{\frac{2^6}{10^6}}=\frac{2}{10}=0.2.

Answer: E.

For theory on exponents and roots check:
math-number-theory-88376.html

For practice on exponents and roots check:
tough-and-tricky-exponents-and-roots-questions-125967.html (DS problems)
tough-and-tricky-exponents-and-roots-questions-125956.html (PS problems)

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COLLECTION OF QUESTIONS:
PS: 1. Tough and Tricky questions; 2. Hard questions; 3. Hard questions part 2; 4. Standard deviation; 5. Tough Problem Solving Questions With Solutions; 6. Probability and Combinations Questions With Solutions; 7 Tough and tricky exponents and roots questions; 8 12 Easy Pieces (or not?); 9 Bakers' Dozen; 10 Algebra set. ,11 Mixed Questions, 12 Fresh Meat

DS: 1. DS tough questions; 2. DS tough questions part 2; 3. DS tough questions part 3; 4. DS Standard deviation; 5. Inequalities; 6. 700+ GMAT Data Sufficiency Questions With Explanations; 7 Tough and tricky exponents and roots questions; 8 The Discreet Charm of the DS ; 9 Devil's Dozen!!!; 10 Number Properties set., 11 New DS set.


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Re: Which of the following is the value of root{3rd rt{0,000064} [#permalink] New post 05 Jun 2013, 03:28
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COLLECTION OF QUESTIONS:
PS: 1. Tough and Tricky questions; 2. Hard questions; 3. Hard questions part 2; 4. Standard deviation; 5. Tough Problem Solving Questions With Solutions; 6. Probability and Combinations Questions With Solutions; 7 Tough and tricky exponents and roots questions; 8 12 Easy Pieces (or not?); 9 Bakers' Dozen; 10 Algebra set. ,11 Mixed Questions, 12 Fresh Meat

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Re: Which of the following is the value of root{3rd rt{0,000064} [#permalink] New post 05 Jun 2013, 08:06
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Which of the following is the value of \sqrt{\sqrt[3]{0.000064}}

(A) 0.004
(B) 0.008
(C) 0.02
(D) 0.04
(E) 0.2

If you know how to do calculations as is, then it is:
\sqrt{\sqrt[3]{0.000064}} = \sqrt{0.04} = 0.2

or

If you know that \sqrt{\sqrt[3]{0.000064}} = \sqrt[6]{0.000064} and 2^6 = 64
Then you can eliminate A, B, and D. Then just move decimals from C and E. C would be 12 decimal places which is WAY too much. 0.2 is 6 which is exactly what you want

Answer is E
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Re: Which of the following is the value of root{3rd rt{0,000064} [#permalink] New post 05 Jun 2013, 17:09
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The above question can be re written as ((10^-6)^1/3)^1/2 * ((64^1/3)^1/2)

= (10^-6)^1/6 * (2^6)^1/6

= 10^1 * 2^1 = 0.2
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Re: Which of the following is the value of root{3rd rt{0,000064} [#permalink] New post 02 Feb 2014, 22:19
Could I just clarify something with a solution to this problem? The explanation in the book was given as: 64 * 10^-6 under the square root and cubed signs (I can't figure out how to write them in). Then from there it goes down to square root of 4 * 10^-2 then 2 * 10^-1 which then equals to .2 which is the answer. I think I've figured out how they got from beginning to end by reading the Number Theory post mentioned at the top, but just need clarification. When you have a base to a fraction power like a^n/m that turns to into n root sign a^m correct? So in this case where you have cubed 10^-6 it would reverse to 10^-6/3 which can be reduced to 10^-2 right? I think that's how the book answer went about getting to .2 but would just like clarification. Also this strategy can be used with any large decimaled number that is under a root or cube sign right?

Thanks for your help!
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Re: Which of the following is the value of root{3rd rt{0,000064} [#permalink] New post 04 Feb 2014, 01:43
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amjet12 wrote:
Could I just clarify something with a solution to this problem? The explanation in the book was given as: 64 * 10^-6 under the square root and cubed signs (I can't figure out how to write them in). Then from there it goes down to square root of 4 * 10^-2 then 2 * 10^-1 which then equals to .2 which is the answer. I think I've figured out how they got from beginning to end by reading the Number Theory post mentioned at the top, but just need clarification. When you have a base to a fraction power like a^n/m that turns to into n root sign a^m correct? So in this case where you have cubed 10^-6 it would reverse to 10^-6/3 which can be reduced to 10^-2 right? I think that's how the book answer went about getting to .2 but would just like clarification. Also this strategy can be used with any large decimaled number that is under a root or cube sign right?

Thanks for your help!


Yes, your reasoning is correct.

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RESOURCES: [GMAT MATH BOOK]; 1. Triangles; 2. Polygons; 3. Coordinate Geometry; 4. Factorials; 5. Circles; 6. Number Theory; 7. Remainders; 8. Overlapping Sets; 9. PDF of Math Book; 10. Remainders; 11. GMAT Prep Software Analysis NEW!!!; 12. SEVEN SAMURAI OF 2012 (BEST DISCUSSIONS) NEW!!!; 12. Tricky questions from previous years. NEW!!!;

COLLECTION OF QUESTIONS:
PS: 1. Tough and Tricky questions; 2. Hard questions; 3. Hard questions part 2; 4. Standard deviation; 5. Tough Problem Solving Questions With Solutions; 6. Probability and Combinations Questions With Solutions; 7 Tough and tricky exponents and roots questions; 8 12 Easy Pieces (or not?); 9 Bakers' Dozen; 10 Algebra set. ,11 Mixed Questions, 12 Fresh Meat

DS: 1. DS tough questions; 2. DS tough questions part 2; 3. DS tough questions part 3; 4. DS Standard deviation; 5. Inequalities; 6. 700+ GMAT Data Sufficiency Questions With Explanations; 7 Tough and tricky exponents and roots questions; 8 The Discreet Charm of the DS ; 9 Devil's Dozen!!!; 10 Number Properties set., 11 New DS set.


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Re: Which of the following is the value of root{3rd rt{0,000064} [#permalink] New post 22 May 2014, 11:20
(64/1000000)^1/6={2^(6)/10^(6)}^1/6 = {2^(6*1/6)/10^(6*1/6)}= 2/10= .2

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Re: Which of the following is the value of root{3rd rt{0,000064} [#permalink] New post 19 Aug 2014, 16:16
This is how I tried it the second time - As long as one is able to find the final exponent on the 10 part of the value, one can simply pick the choice that matches that exponent value. In this case 10^(-6)*(1/6) = 1/10 = 0.1 and the only choice that has one decimal place is E.
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Re: Which of the following is the value of root{3rd rt{0,000064} [#permalink] New post 19 Aug 2014, 21:04
Bunuel wrote:
Which of the following is the value of \sqrt{\sqrt[3]{0.000064}}

(A) 0.004
(B) 0.008
(C) 0.02
(D) 0.04
(E) 0.2

Practice Questions
Question: 9
Page: 153
Difficulty: 650


\sqrt{\sqrt[3]{0.000064}} = \sqrt[(2*3)]{\frac{64}{10^6}} = (\frac{2^6}{10^6})^{\frac{1}{6}} = \frac{2}{10} = 0.2

Answer = E

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Re: Which of the following is the value of root{3rd rt{0,000064}   [#permalink] 19 Aug 2014, 21:04
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