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The square of 5^(root2)

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The square of 5^(root2)  [#permalink]

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New post 12 Jan 2012, 08:03
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Question Stats:

53% (00:55) correct 47% (01:04) wrong based on 197 sessions

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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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Re: the square of 5  [#permalink]

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New post 12 Jan 2012, 08:18
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manalq8 wrote:
The square of \(5^{\sqrt{2}}\) = ?

\(5^2\)
\(25^{\sqrt{2}}\)
\(25\)
\(25^{2\sqrt{2}}\)
\(5^{\sqrt{2}^2}\)


Question: \((5^{\sqrt{2}})^2=?\).

\((5^{\sqrt{2}})^2=5^{2*\sqrt{2}}=(5^2)^{\sqrt{2}}=25^{\sqrt{2}}\).

Answer: B.

For theory on exponents and roots check: math-number-theory-88376.html
For practice on exponents and roots check: tough-and-tricky-exponents-and-roots-questions-125967.html (DS problems) and tough-and-tricky-exponents-and-roots-questions-125956.html (DS problems).

Hope it helps.
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Re: the square of 5  [#permalink]

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New post 12 Jul 2012, 03:01
Bunuel wrote:
manalq8 wrote:
The square of \(5^{\sqrt{2}}\) = ?

\(5^2\)
\(25^{\sqrt{2}}\)
\(25\)
\(25^{2\sqrt{2}}\)
\(5^{\sqrt{2}^2}\)


Question: \((5^{\sqrt{2}})^2=?\).

\((5^{\sqrt{2}})^2=5^{2*\sqrt{2}}=(5^2)^{\sqrt{2}}=25^{\sqrt{2}}\).

Answer: B.

For theory on exponents and roots check: math-number-theory-88376.html
For practice on exponents and roots check: tough-and-tricky-exponents-and-roots-questions-125967.html (DS problems) and tough-and-tricky-exponents-and-roots-questions-125956.html (DS problems).

Hope it helps.


Is this a 700 level question??
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Re: the square of 5  [#permalink]

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New post 12 Jul 2012, 03:10
MacFauz wrote:
Bunuel wrote:
manalq8 wrote:
The square of \(5^{\sqrt{2}}\) = ?

\(5^2\)
\(25^{\sqrt{2}}\)
\(25\)
\(25^{2\sqrt{2}}\)
\(5^{\sqrt{2}^2}\)


Question: \((5^{\sqrt{2}})^2=?\).

\((5^{\sqrt{2}})^2=5^{2*\sqrt{2}}=(5^2)^{\sqrt{2}}=25^{\sqrt{2}}\).

Answer: B.

For theory on exponents and roots check: math-number-theory-88376.html
For practice on exponents and roots check: tough-and-tricky-exponents-and-roots-questions-125967.html (DS problems) and tough-and-tricky-exponents-and-roots-questions-125956.html (DS problems).

Hope it helps.


Is this a 700 level question??


I'd say that this is a 600 level question. Edited difficulty tag.
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Re: The square of 5^(root2)  [#permalink]

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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: The square of 5^(root2)  [#permalink]

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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: The square of 5^(root2)  [#permalink]

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New post 19 Apr 2019, 05:00
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Re: The square of 5^(root2)   [#permalink] 19 Apr 2019, 05:00
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