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Which of the following is the value of root{3rd rt{0,000064}
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30 Jul 2012, 02:02
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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 Practice Questions Question: 9 Page: 153 Difficulty: 650
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Re: Which of the following is the value of root{3rd rt{0,000064}
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30 Jul 2012, 02:02
SOLUTIONWhich 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: mathnumbertheory88376.htmlFor practice on exponents and roots check: toughandtrickyexponentsandrootsquestions125967.html (DS problems) toughandtrickyexponentsandrootsquestions125956.html (PS problems)
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Re: Which of the following is the value of root{3rd rt{0,000064}
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30 Jul 2012, 02:39
(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}
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30 Jul 2012, 03:04
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}
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05 Jun 2013, 04:28
Bumping for review and further discussion*. Get a kudos point for an alternative solution! *New project from GMAT Club!!! Check HERE
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Re: Which of the following is the value of root{3rd rt{0,000064}
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05 Jun 2013, 09:06
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}
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05 Jun 2013, 18:09
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}
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02 Feb 2014, 23:19
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}
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04 Feb 2014, 02:43
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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Re: Which of the following is the value of root{3rd rt{0,000064}
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19 Aug 2014, 22:04
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}
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09 Dec 2014, 20:26
cube root of 64 is 4. because we need the cube root of 0.000064, 4 needs to have (1/3) as many digits to the right of the decimal as 64, so 0.04.
Similarly, we need the square root of 0.04, so the square root of 4 is 2, but we need half the digits to the right of the decimal, so 0.2



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Re: Which of the following is the value of root{3rd rt{0,000064}
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11 Apr 2016, 16:30
Attached is a visual that should help.
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Re: Which of the following is the value of root{3rd rt{0,000064}
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03 May 2016, 08:55
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
Solution: Let's review the notation first. When an exponent is a fraction, that exponent indicates taking a root. So if we have, for example, 27^1/3, the 1/3 instructs us to take the cube root of 27, which is 3. Similarly, if the exponent were 1/2, such as in 25^1/2, the 1/2 instructs us to take the square root of 25, which is 5. To solve this question, we can refer to two rules: 1) If a decimal with a finite number of decimal places is a perfect cube, its cube root will have exactly onethird of the number of decimal places. Thus, a perfect cube decimal must have a number of decimal places that is a multiple of 3. 2) If a decimal with a finite number of decimal places is a perfect square, its square root will have exactly half of the number of decimal places. Thus, a perfect square decimal must have an even number of decimal places. Let's look first at (0.000064)^1/3. The 1/3 instructs us to take the cube root of 0.000064. By rule number 1, the cube root of 0.000064 = 0.04. We were able obtain this value because 0.000064 has 6 DECIMAL PLACES and because the cube root of 64 is 4. The problem now looks like this: (0.04)^1/2. The ½ instructs us to find the square root of 0.04. By rule number 2, the square root of 0.04 = 0.2. We were able to obtain this value because 0.04 has 2 DECIMAL PLACES and the square root of 4 is 2. Answer E.
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Re: Which of the following is the value of root{3rd rt{0,000064}
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30 May 2016, 20:53
(3√0,000064)^(1/2) Or [(0.000064)^(1/3) ]^(1/2)
Start from the inner most value.
0.000064 = 64/1000000 (0.000064)^(1/3) = 4/100 {(0.000064)^(1/3) ]^(1/2) = (4/100)^(1/2) = 2/10
Correct Option: E



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Re: Which of the following is the value of root{3rd rt{0,000064}
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18 Jun 2016, 19:21
Here is another version..
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Re: Which of the following is the value of root{3rd rt{0,000064}
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Re: Which of the following is the value of root{3rd rt{0,000064}
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