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Which of the following is equal to the square of 5^(root2)

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manalq8
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Which of the following is equal to the square of 5^(root2) [#permalink] New post   12 Jan 2012, 08:03
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Which of the following is equal to the square of \(5^{\sqrt{2} }\)?

A. \(5^2\)

B. \(25^{\sqrt{2} }\)

C. \(25\)

D. \(25^{2\sqrt{2} }\)

E. \(5^{\sqrt{2}^2}\)

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Which of the following is equal to the square of 5^(root2) [#permalink] New post   12 Jan 2012, 08:18
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Which of the following is equal to the square of \(5^{\sqrt{2} }\)?

A. \(5^2\)
B. \(25^{\sqrt{2} }\)
C. \(25\)
D. \(25^{2\sqrt{2} }\)
E. \(5^{\sqrt{2}^2}\)


We need to determine the value of \((5^{\sqrt{2} })^2\). Remember, according to exponent rules, \((a^m)^n = a^{mn}\), (whereas \(a^{m^n} = a^{(m^n)}\)). Therefore:

\((5^{\sqrt{2} })^2=\)

\(=5^{2*\sqrt{2} }=\)

\(=(5^2)^{\sqrt{2} }=\)

\(=25^{\sqrt{2} }\).


Answer: B

For theory on exponents and roots check: https://gmatclub.com/forum/math-number- ... 88376.html
For practice on exponents and roots check: https://gmatclub.com/forum/tough-and-tr ... 25967.html (DS problems) and https://gmatclub.com/forum/tough-and-tr ... 25956.html (DS problems).

Hope it helps.
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sanjoo
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Re: Which of the following is equal to the square of 5^(root2) [#permalink] New post   12 Jul 2012, 11:01
Bunuell i think its ans is 50.. which is not given in options..


square of square root 2 will only 2.. 5^2 will be 25.. 2 multiply by 25 will be 50..

where i m wrong??
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Re: Which of the following is equal to the square of 5^(root2) [#permalink] New post   12 Jul 2012, 12:36
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sanjoo wrote:
Bunuell i think its ans is 50.. which is not given in options..


square of square root 2 will only 2.. 5^2 will be 25.. 2 multiply by 25 will be 50..

where i m wrong??


Note that:
\((a^m)^n=a^{mn}\)
and
\(a^m^n=a^{(m^n)}\) (if exponentiation is indicated by stacked symbols, the rule is to work from the top down).

So, \((5^{\sqrt{2}})^2=5^{2*\sqrt{2}}\) and not \(5^{\sqrt{2}^2\).

Also even if we had \(5^{\sqrt{2}^2\) the answer sill wouldn't be 50 it would be 25: \(5^{\sqrt{2}^2=5^{({\sqrt{2}^2)}==5^2=25\).

For more check Number Theory chapter of Math Book: math-number-theory-88376.html

Hope it helps.
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Re: Which of the following is equal to the square of 5^(root2) [#permalink] New post   07 Oct 2023, 15:49
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