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

1

This post received KUDOS

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

Re: Which of the following is the value of root{3rd rt{0,000064} [#permalink]
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?

Re: Which of the following is the value of root{3rd rt{0,000064} [#permalink]
04 Feb 2014, 01:43

Expert's post

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?

Re: Which of the following is the value of root{3rd rt{0,000064} [#permalink]
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.