The Square of 5^√2 =? GMAT Problem Solving

Question: The Square of 5^√2 =?

1. \(5^2\)
2. \(25^\sqrt2\)
3. 25
4. \(25^{2\sqrt2}\)
5. \(5^{\sqrt2^2}\)

‘The square of \(5^\sqrt2\) =?’ - is a topic of the GMAT Quantitative reasoning section of GMAT. This question has been taken from the book “ GMAT Prep”. To solve GMAT Problem Solving questions a student must have knowledge about a good amount of qualitative skills. The GMAT Quant topic in the problem-solving part requires calculative mathematical problems that should be solved with proper mathematical knowledge.

Solution and Explanation:

Approach Solution 1:

It is asked in the question to find out the value of square of 5^√2.

Squaring this number we get,

\((5^{\sqrt2}){^2}\)

There is a property that says,

\((a^{m}){^n}\) = \((a^{n}){^m}\) = \(a^{m*n}\)

Here m = 2 , n = 2 and a = 5
We get,

\((5^{\sqrt2}){^2}\) =\(5^{2\sqrt2}\)

\(5^{2\sqrt2}\)is of the form \(a^{m*n}\)

Here m = 2 and n = 2

We can write it as \(a^{m*n}\) = \((a^{m}){^n}\)

\(5^{2\sqrt2}\) =\((5^{2}){^\sqrt2}\) = \(25^\sqrt2\)

Therefore the correct answer will be option B.

Correct Answer: B

Approach Solution 2:

It is asked in the question to find out the value of square of 5^√2.

Squaring this number we get,

\((5^{\sqrt2}){^2}\)

There is a property that says,

\((a^{m}){^n}\) =\((a^{n}){^m}\)= \(a^{m*n}\)

We can interchange the powers of the numbers

We are given,

\((5^{\sqrt2}){^2}\) =\((5^{2}){^\sqrt2}\) =\((5*5)^\sqrt2\)=\(25^\sqrt2\)

Therefore the correct answer will be option B.

Correct Answer: B

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