Question

Which shows the following radical expression in simplified radical form with the smallest possible index?

Answer 1

Here's the expression:
\[^{6}\sqrt{24^{2}}\]

Answer 2

Here's the choices I have:
A. \[2 ^{3}\sqrt{3}\]
B. \[3^{3}\sqrt{4}\]
C. \[4^{3}\sqrt{3}\]
D. \[6^{3}\sqrt{4}\]

Answer 3

Do you know you can re-write a "6th root" as the exponent 1/6 ?
in other words
\[\sqrt[6]{24^2}= \left( 24^2 \right)^\frac{1}{6}= 24^{2 \cdot \frac{1}{6}}= 24^\frac{1}{3}\]

Answer 4

You are looking for the cube root (that is the other way to think of to the power 1/3)
of 24

factor 24 into its prime factors, and look for triples of the same number to "pull out"

Answer 5

Ohh!! Okay! I completely forgot that could be done! Thank you so much for the refresher! (:

Answer 6

24 = 2*12= 2*2*6= 2*2*2*3

you have a triple of 2's that you can pull out of the cube root sign

Answer 7

So would the answer be A?

Answer 8

\[ \sqrt[3]{2 \cdot 2 \cdot 2 \cdot 3} =\sqrt[3]{2 \cdot 2 \cdot 2 } \cdot \sqrt[3]{3} = 2 \sqrt[3]{3}\]

Answer 9

Okay! Thank you so much for the help (: I really do appreciate it!