SOLUTION: Problem 1 Have I simplified the radical expressions below by rationalizing the denominators correctly? An index to left of radical sign is a 3. The radicand (square root) is

Question 1173909: Problem 1
Have I simplified the radical expressions below by rationalizing the denominators correctly?
An index to left of radical sign is a 3. The radicand (square root) is 24/125. 3/24 3/125 5/5 = 120/125 = Index 3 120/5
Problem 2:
An index to left of radical sign is a 3. The radicand (square root) is 2/3. 2/3 3/3 = 6/27 = Index 3 6/3
If I have not done this correctly, please show me where I have not simplified these 2 radical expressions via rationalizing their denominators.
Thank you

Found 3 solutions by Boreal, ewatrrr, MathTherapy:
Answer by Boreal(15235)   (Show Source): You can put this solution on YOUR website!
index 2 is square root; index 3 is cube root
I will write as fractional exponents
24^(1/3)/125^(1/3)
the denominator is 5
the numerator is 8^(1/3)*3^(1/3) or 2*3^(1/3)
=(2/5)*3^(1/3)
I can't follow what you did to get 120/125. Cube root of 120 is 8^(1/3)*15^(1/3)=2*15^(1/3)
-
cube root of (2/3)=2^(1/3)/3^(1/3)
multiply top and bottom by 3^(2/3), which makes the denominator 3.
numerator is 2^(1/3)*3^(2/3) and can also write as 6^(1/3)*3^(1/3)=18^(1/3)
18^(1/3)/3. Don't cancel.
Answer by ewatrrr(24785)   (Show Source): You can put this solution on YOUR website!

Hi,
Know it is difficult to get symbols to make the trip:
((24/125)(3/24)(3/125)(5/5))^1/2 that works

3/125 is the simplification (no radical sign in the denominator)

2/3 the simplification (again , no radical sign present in the denominator)
Wish You the Best in your Studies.

Answer by MathTherapy(10552)   (Show Source): You can put this solution on YOUR website!

Problem 1
Have I simplified the radical expressions below by rationalizing the denominators correctly?
An index to left of radical sign is a 3. The radicand (square root) is 24/125. 3/24 3/125 5/5 = 120/125 = Index 3 120/5
Problem 2:
An index to left of radical sign is a 3. The radicand (square root) is 2/3. 2/3 3/3 = 6/27 = Index 3 6/3
If I have not done this correctly, please show me where I have not simplified these 2 radical expressions via rationalizing their denominators.
Thank you

Are these what you have: , and ?
I don't see these expressions as being in the category where their denominators need to be rationalized.
It appears as though you multiplied by and for no reason at all. If I'm correct, then your expressions should be:
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