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√m4=64 and m>0, what is the value of cubic root of m?

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√m4=64 and m>0, what is the value of cubic root of m?  [#permalink]

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New post 06 Jul 2017, 01:27
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\(√m^4=64\) and m>0, what is the value of cubic root of m?

A. 1
B. 2
C. 4
D. 8
E. 16

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√m4=64 and m>0, what is the value of cubic root of m?  [#permalink]

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New post 06 Jul 2017, 02:34
Since \(√m^4=64\),
\(m^2\) will be equal to 64.
m can take value 8 or -8(which is eliminated as m>0)

Therefore, m=8
The cube root of m is 2(Option B)
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Re: √m4=64 and m>0, what is the value of cubic root of m?  [#permalink]

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New post 06 Jul 2017, 03:08
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Re: √m4=64 and m>0, what is the value of cubic root of m?  [#permalink]

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New post 06 Jul 2017, 03:36
MathRevolution wrote:
\(√m^4=64\) and m>0, what is the value of cubic root of m?

A. 1
B. 2
C. 4
D. 8
E. 16


\(\sqrt{m^{4}} = 64.\)
Squaring on both sides, we get \(m^{4} = 64^{2}\)
So, \(m^{2} = 64\), hence, \(m = 8\) (given: \(m > 0\))

Cube root of 8 = 2. Ans - B.
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Re: √m4=64 and m>0, what is the value of cubic root of m?  [#permalink]

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New post 06 Jul 2017, 04:46
1
MathRevolution wrote:
\(√m^4=64\) and m>0, what is the value of cubic root of m?

A. 1
B. 2
C. 4
D. 8
E. 16


\(\sqrt{m^4}=64\)

\(m^{\frac{4}{2}}\) \(= 64\)

\(m^2 = 64\)

\(m = +8\) or \(-8\)

Given \(m>0\).

Therefore; \(m = 8\)

We need to find the value of Cubic root of \(m\)

\(\sqrt[3]{m} = \sqrt[3]{8} = 2\)

Answer (B)...

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Re: √m4=64 and m>0, what is the value of cubic root of m?  [#permalink]

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New post 06 Jul 2017, 08:07
MathRevolution wrote:
\(√m^4=64\) and m>0, what is the value of cubic root of m?

A. 1
B. 2
C. 4
D. 8
E. 16


\(√m^4=64\)

So, \(√m^2=8^2\)

Or, \(m = 8\)

Hence, \(^3√m=2\)

Thus, answer will be (B) 2
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Re: √m4=64 and m>0, what is the value of cubic root of m?  [#permalink]

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New post 09 Jul 2017, 18:26
==> You get \(√m^4=64=2^6, m^4=(2^6)^2=2^{12}.\) Then, you get \(m=(2^{12})^{\frac{1}{4}}=2^3\), and from 3√m=3\(\sqrt{2^3}\)=2, the answer is B.

Answer: B
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Re: √m4=64 and m>0, what is the value of cubic root of m?  [#permalink]

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New post 14 Jul 2017, 10:36
MathRevolution wrote:
\(√m^4=64\) and m>0, what is the value of cubic root of m?

A. 1
B. 2
C. 4
D. 8
E. 16


Let’s solve for m:

√(m^4) = 64

(m^4)^(½) = 64

m^2 = 64

|m| = √64

|m| = 8

m = 8 or m = -8

Since m > 0, m = 8.

Thus, the cube root of m is 2.

Answer: B
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Re: √m4=64 and m>0, what is the value of cubic root of m?   [#permalink] 14 Jul 2017, 10:36
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