The square of \(5^\sqrt2\) =?

Question: The square of \(5^\sqrt2\) =?

1. \(5^2\)
2. \(25^\sqrt2\)
3. 25
4. \(5^{{2}\sqrt2}\)
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 Quantitative Review". GMAT Quant section consists of a total of 31 questions. To solve GMAT Problem Solving questions a student must have knowledge about a good number of qualitative skills. The GMAT quant topics in the problem-solving part require calculative mathematical problems that should be solved with proper mathematical knowledge.

Answer:

Write down the original equation and put it equal to x, we will get:

x = \({(5^\sqrt2)}^2\)

This expression can be written as:

x = \(5^\sqrt2 * 5^\sqrt2\)

As we know that when bases are same and they are multiplied with each other, we can add the powers. So, in the question, we will get:

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

Square of 5 is 25, so the above formed expression can be written as:

x = \(25^\sqrt2\)

Correct Answer: B

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