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

Algebra ->  Radicals -> 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      Log On


   

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) About Me  (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)
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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) About Me  (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)

sqrt%28%282%2F3%29%282%2F3%29+%28cross%283%29%2Fcross%283%29%29%29+=+sqrt%284%2F9%29+=+2%2F3

2/3 the simplification (again , no radical sign present in the denominator)

Wish You the Best in your Studies.

Answer by MathTherapy(10552) About Me  (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: root%283%2C+%2824%2F125%29%283%2F24%29%283%2F125%29%285%2F5%29%29, and root%283%2C+%282%2F3%29%282%2F3%29%283%2F3%29%29?

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 5%2F5 and 3%2F3 for no reason at all. If I'm correct, then your expressions should be: