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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?