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# What is the value of [m](\sqrt[3]{\sqrt{\sqrt[3]{512}}})^2[/m]

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Math Expert
Joined: 02 Sep 2009
Posts: 46194
What is the value of [m](\sqrt[3]{\sqrt{\sqrt[3]{512}}})^2[/m] [#permalink]

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10 May 2017, 11:57
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Difficulty:

5% (low)

Question Stats:

84% (01:11) correct 16% (01:16) wrong based on 93 sessions

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What is the value of $$(\sqrt[3]{\sqrt{\sqrt[3]{512}}})^2$$?

A. 1/16

B. 1/8

C. 1/2

D. 2

E. 8

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Re: What is the value of [m](\sqrt[3]{\sqrt{\sqrt[3]{512}}})^2[/m] [#permalink]

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10 May 2017, 12:53
1
Bunuel wrote:
What is the value of $$(\sqrt[3]{\sqrt{\sqrt[3]{512}}})^2$$?

A. 1/16

B. 1/8

C. 1/2

D. 2

E. 8

Expression will become 512^(2*1/3*1/2*1/3)

So we are left with (512)^(1/3*1/3)

cube root of 512 is 8. So we are now left with 8^1/3 which is 2.

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What is the value of [m](\sqrt[3]{\sqrt{\sqrt[3]{512}}})^2[/m] [#permalink]

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11 May 2017, 03:17
1
Bunuel wrote:
What is the value of $$(\sqrt[3]{\sqrt{\sqrt[3]{512}}})^2$$?

A. 1/16

B. 1/8

C. 1/2

D. 2

E. 8

$$(\sqrt[3]{\sqrt{\sqrt[3]{512}}})^2$$ -------(cube root of 512 = 8)
= $$(\sqrt[3]{\sqrt8})^2$$ ------- (squaring $$(\sqrt{8})^2$$ we get 8 )
= $$(\sqrt[3]{8})$$
= $$(\sqrt[3]{8})$$ = 2

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Re: What is the value of [m](\sqrt[3]{\sqrt{\sqrt[3]{512}}})^2[/m] [#permalink]

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11 May 2017, 04:52
512 = 8*8*8..

hence solving the expression gives as 2

ans D
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What is the value of [m](\sqrt[3]{\sqrt{\sqrt[3]{512}}})^2[/m] [#permalink]

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11 May 2017, 09:30
Bunuel wrote:
What is the value of $$(\sqrt[3]{\sqrt{\sqrt[3]{512}}})^2$$?

A. 1/16

B. 1/8

C. 1/2

D. 2

E. 8

$$\Bigg (\sqrt[3]{\sqrt{\sqrt[3]{512}}}\Bigg )^2=\bigg (\sqrt[3]{\sqrt{8}} \bigg )^2 \\ = \bigg (\sqrt[3]{\sqrt{2^3}} \bigg )^2=\big (\sqrt{2} \big )^2=2$$

Or we could solve in this way:

$$\Bigg (\sqrt[3]{\sqrt{\sqrt[3]{512}}}\Bigg )^2 =\Bigg (\sqrt[3]{\sqrt{512^{\frac{1}{3}}}}\Bigg )^2 \\ = \Bigg (\sqrt[3]{\Big ( 512^{\frac{1}{3}} \Big )^{\frac{1}{2}}}\Bigg )^2 = \Bigg (\sqrt[3]{ 512^{\frac{1}{6}} }\Bigg )^2 \\ = \Bigg ( \Big (512^{\frac{1}{6}} \Big ) ^ {\frac{1}{3}}\Bigg )^2 = \Bigg ( 512^{\frac{1}{18}}\Bigg )^2 \\ = 512^{\frac{1}{9}} = (2^9)^{\frac{1}{9}} = 2$$
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Re: What is the value of [m](\sqrt[3]{\sqrt{\sqrt[3]{512}}})^2[/m] [#permalink]

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11 May 2017, 09:48
Bunuel wrote:
What is the value of $$(\sqrt[3]{\sqrt{\sqrt[3]{512}}})^2$$?

A. 1/16

B. 1/8

C. 1/2

D. 2

E. 8

Every cube root can be replaced by 1/3 and square root can be replaced by 1/2 in the power.

$$512 = 2^9$$

$$(\sqrt[3]{\sqrt{\sqrt[3]{512}}})^2$$

$$= (2^9)^{2*(1/3)*(1/2)*(1/3)}$$

$$= 2$$
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Re: What is the value of [m](\sqrt[3]{\sqrt{\sqrt[3]{512}}})^2[/m] [#permalink]

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12 May 2017, 04:23
Bunuel wrote:
What is the value of $$(\sqrt[3]{\sqrt{\sqrt[3]{512}}})^2$$?

A. 1/16

B. 1/8

C. 1/2

D. 2

E. 8

$$(\sqrt[3]{\sqrt{\sqrt[3]{512}}})^2$$
= (512)^(2*1/3*1/2*1/3)
= (512)^1/9
= 2

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Re: What is the value of [m](\sqrt[3]{\sqrt{\sqrt[3]{512}}})^2[/m] [#permalink]

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27 May 2018, 01:54
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Re: What is the value of [m](\sqrt[3]{\sqrt{\sqrt[3]{512}}})^2[/m]   [#permalink] 27 May 2018, 01:54
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