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# The square of 5^(root2)

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12 Jan 2012, 08:03
1
3
00:00

Difficulty:

45% (medium)

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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12 Jan 2012, 08:18
3
2
manalq8 wrote:
The square of $$5^{\sqrt{2}}$$ = ?

$$5^2$$
$$25^{\sqrt{2}}$$
$$25$$
$$25^{2\sqrt{2}}$$
$$5^{\sqrt{2}^2}$$

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

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

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

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

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

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

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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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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12 Jul 2012, 12:36
1
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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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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