SOLUTION: Simplify the following expression by rationalizing the denominator. Write the result in simplest form. 3 over the cube root of 2

Algebra ->  Algebra  -> Rational-functions -> SOLUTION: Simplify the following expression by rationalizing the denominator. Write the result in simplest form. 3 over the cube root of 2      Log On

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Question 77815: Simplify the following expression by rationalizing the denominator. Write the result in simplest form.
3 over the cube root of 2
Found 2 solutions by Earlsdon, ptaylor:
Answer by Earlsdon(6103) About Me  (Show Source):
You can put this solution on YOUR website!
Simplify:
3%2F2%5E%281%2F3%29 It is simpler to use the exponential form of the cube root of 2.
Multiply the fraction by 2%5E%282%2F3%29%2F2%5E%282%2F3%29
3%282%5E%282%2F3%29%29%2F%282%5E%281%2F3%29%29%282%5E%282%2F3%29%29 Simplifying this, we get:
3%284%5E%281%2F3%29%29%2F2
You can read this as: 3 times the cube root of 4 all over 2.

Answer by ptaylor(1894) About Me  (Show Source):
You can put this solution on YOUR website!
3/(cube root of 2) can be written as 3/(2^(1/3)). Now lets multiply both numerator and denominator by (2^(2/3)) to get rid of the exponent in the denominator. Remember, when we multiply exponents, we add them.
And we get:
((3)(2^(2/3)))/(2^(1/3+2/3))=
((3)(cube root of 2^2))/2=
((3)(cube root of (4))/2 or ((3)(4^(1/3)))/2-------------------ans
CK
Use calculator to check your answer

Hope this helps-----ptaylor