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Simplify and rationalize the denominator: $\sqrt[3]{\frac{8}{\sqrt{27}}}.$ If the simplified expression can be expressed in the form $\frac{a\sqrt{b}}{c}$, what is a+b+c?

Jun 10, 2019

#1
+30
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ahhh the formatting is scary but here we go! $$\sqrt[3]{\frac{8}{\sqrt{27}}}$$  $$\frac{a\sqrt{b}}{c}, a+b+c?$$
Ok so first you need to simpify the first expression which is 2/3 because
cube root of 8= 2
so next you would need to say that radical 27 is basically 27 to the power of 1/2 and put it under the cube root and simplify
and you would get $$2\sqrt{3}/3$$ and then you need to add the 3 numbers so it would be 8.
(´･ω･) (´･ω･) (´･ω･`)

Jun 11, 2019
#2
+248
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Thanks!

sinclairdragon428  Jun 11, 2019