Which of the following is equal to the square of 5^(root2)

Question

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}

Bunuel · Accepted Answer

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.

Bunuel · Answer

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.

sanjoo · Answer

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??

TheRomanRoyalty · Answer

I'm not sure I understand this question. Can't we just rewrite radical 2 as 1.4. 
How can 5 raised to 1.4 be the same as 25 raised to 1.4?

Bunuel · Answer

First of all, \sqrt{2} is approximately 1.4. Next, plese review the solution below carefully. Hope it helps. 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.

justcallmedaniel · Answer

I was confused with this question because I missed an important piece of information which is equal to (5^(root2))^2, This question is testing exponent rules and the question is asking for what is equal to and not what the approximation is. 1.4 is the approximation of root2 but in reality is not 1.4. Hope that helps!

TheRomanRoyalty

I'm not sure I understand this question. Can't we just rewrite radical 2 as 1.4.
How can 5 raised to 1.4 be the same as 25 raised to 1.4?

Bixy34 · Answer

Hi  Bunuel , I understood the solution here but I have 1 doubt ~ how did you determine that 5 root 2 square would be 5 raised to the power 2 root two and not 5 root 2 whole square (In which case I believe visually it seems to me that the 2nd exponent rule of a raised to the power m raised to the power n would apply? Can you clarify?

Bunuel · Answer

Because the square of  5^{\sqrt{2} }  means  (5^{\sqrt{2}})^2 .

Saks116 · Answer

Use the exponential property to ￼(a^m￼)^n =a^mn

Or

In case you don’t remember

Let (5)^sq root(2) =x 
Square both side 
You need to find value of x ^2

Solve it you will get 25^sq root(2)

Which of the following is equal to the square of 5^(root2)

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Which of the following is equal to the square of 5^(root2)

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