logo for solving-math-problems.com
leftimage for solving-math-problems.com

College Algebra - Simplify Radical Expression

by Sasha
(Evansville, IN, US)











































how to simplify cubed root of 3x^2 divided by the cubed root of 24x^5

Comments for College Algebra - Simplify Radical Expression

Click here to add your own comments

Sep 07, 2011
Simplify Radical Expression
by: Staff


The question:

by Sasha
(Evansville, IN, US)

how to simplify cubed root of 3x^2 divided by the cubed root of 24x^5


The answer:

3x^2 divided by the cubed root of 24x^5

[∛(3x²)]/[∛(24x⁵)]


You can use either the law of exponents or the distributive law to simplify this expression.

Using the distributive law for radicals, you can combine both the numerator and denominator under a single radical sign

[∛(3x²)]/[∛(24x⁵)]

= ∛[(3x²)/(24x⁵)]


You now have a single fraction under a single radial sign.

Since you are able to cancel factors which appear in the numerator and denominator of any fraction, you can cancel common factors for this fraction as well.

= ∛[(3x²)/(24x⁵)]

= ∛[(3*x²)/(3*8*x²*x³)]

= ∛{(3 / 3) * (x² / x²) * [1 / (8*x³)]}

= ∛{(1) * (1) * [1 / (8*x³)]}

= ∛[1 / (8*x³)]


Take the cube root of the expression which remains

= ∛[1 / (8*x³)]

= ∛[1 / (2³*x³)]


Using the distributive law for radicals again, you can separate the radical which applies to the numerator from the radical which applies to the denominator.

= ∛[1 / (2³*x³)]

= ∛(1) / ∛(2³*x³)]


Take the cube root of the numerator

= ∛(1) / ∛(2³*x³)]

= 1 / ∛(2³*x³)]


Take the cube root of the denominator

= 1 / ∛(2³*x³)]

= 1 / (2*x)

= 1 / (2x)



The final answer is: 1 / (2x)




Thanks for writing.

Staff
www.solving-math-problems.com



Click here to add your own comments

Join in and write your own page! It's easy to do. How? Simply click here to return to Math Questions & Comments - 01.



Copyright © 2008-2015. All rights reserved. Solving-Math-Problems.com