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12 Jan 2012, 08:03
Kudos
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B
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Difficulty:
45%
(medium)
Question Stats:
60% (01:01) correct
40%
(01:11)
wrong
based on 1826
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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. \(5^{\sqrt{2}^2}\)
A. \(5^2\)
B. \(25^{\sqrt{2} }\)
C. \(25\)
D. \(25^{2\sqrt{2} }\)
E. \(5^{\sqrt{2}^2}\)
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12 Jan 2012, 08:18
Kudos
Bookmarks
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.
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.
12 Jul 2012, 12:36
Kudos
Bookmarks
sanjoo
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: https://gmatclub.com/forum/math-number- ... 88376.html
Hope it helps.
