Perform the indicated operation and express your answer in simplest radical form.
^3√8
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^4√8
a)12√64
b)12√8
c)-√8
d)7√8
Sorry....your question doesn't make any sense to me....did you leave something out????
Let me just understand what you are trying to obtain: do you want the answer in "simplest radical form" to this expression: 3r.root of 8 DIVIDED by the 4th. root of 8? If that's what you are trying to get, the answer I gave you is the correct answer. It can't "b", because if you calculate it on a calculator, you get: 12 X 2.828427(or square root of 8)=33.941125.....etc.
Here is your answer step by step:
Simplify the following:
(8^(1/3))/(8^(1/4))
Simplify radicals.
8^(1/4) = (2^3)^(1/4):
(8^(1/3))/(2^(3/4))
Simplify radicals.
8^(1/3) = (2^3)^(1/3) = 2:
2/2^(3/4)
Multiply numerator and denominator of 2/2^(3/4) by 2^(1/4).
Rationalize the denominator. 2/2^(3/4) = 2/2^(3/4)×(2^(1/4))/(2^(1/4)) = (2 2^(1/4))/(2):
(2 2^(1/4))/(2)
Cancel common terms in the numerator and denominator of (2 2^(1/4))/(2).
(2 2^(1/4))/(2) = 2/2×2^(1/4) = 2^(1/4):
Answer:
2^(1/4)