If x^2 = 2^(1/2), then x^8 =

Question

If x^2 = \sqrt{2} , then x^8 = A. 2^{\sqrt{2}} B. 4 C. 4^{\sqrt{2}} D. 8 E. 16 2024-01-28_20-41-00.png

Bunuel · Answer

x^8 =(x^2)^4

x^8 =(\sqrt{2})^4=(\sqrt{2})(\sqrt{2})(\sqrt{2})(\sqrt{2})

x^8 =4

Answer: B.

nurbijoy · Answer

x^2 = \sqrt{2}
x = 2^(1/4)
So, x^8 = (2^(1/4))^8
 = 2^2
 = 4

A_Nishith · Answer

x^8=(x^2)^4

x^8=(√2)^4=(√2)(√2)(√2)(√2)

x^8=4

Answer: B.

DanTheGMATMan · Answer

Don't solve for x, just keep it simple and create x^8:

https://www.youtube.com/watch?v=ez6sM0IvBNE

GmatKnightTutor · Answer

For this question, it may first help to SQUARE the expression ( x^2 = \sqrt{2} ) on both sides:

(x^2)^2 = (\sqrt{2} )^2  ---->   x^4 = 2

If we SQUARE both sides again, we get

(x^4)^2 = (2)^2  ---->  x^8 = 4

(B) is your answer.

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