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s2001
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M06-20 25 May 2026, 19:48
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I like the solution - it’s helpful.
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SportDice
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M06-20 05 Jun 2026, 12:23
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How are we going from 5^(sqrt2) in the question to 5^((sqrt2)*2) in the solution?
Bunuel
Official Solution:

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
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Bunuel
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M06-20 05 Jun 2026, 13:25
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SportDice
How are we going from 5^(sqrt2) in the question to 5^((sqrt2)*2) in the solution?
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The question asks for the square of \(5^{\sqrt{2} }\), so we need to square the entire expression:

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

Using the exponent rule \((a^m)^n = a^{mn}\), we get:

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

So the exponent becomes \(\sqrt{2}*2\) because the whole expression is being squared.
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TruePen
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M06-20 25 Jun 2026, 02:08
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I like the solution - it’s helpful.
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TruePen
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M06-20 25 Jun 2026, 02:08
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I like the solution - it’s helpful.
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GooDMan5212
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M06-20 27 Jul 2026, 12:56
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I did not quite understand the question. question show incorrect value, = it should be (5 ^sqrt2)^2, but for me it was shown as 5^sqrt2
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Bunuel
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M06-20 27 Jul 2026, 13:03
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GooDMan5212
I did not quite understand the question. question show incorrect value, = it should be (5 ^sqrt2)^2, but for me it was shown as 5^sqrt2
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Please check the question:

Which of the following is equal to the square of \(5^{\sqrt{2} }\)?

Now, review the solution again. Hope this helps.
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Janejane02
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M06-20 19 Aug 2026, 02:40
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I like the solution - it’s helpful.
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