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Tuesday, June 18, 2013

Algebraic Operations - Radicals, 3

Category: Algebra, Arithmetic

"Published in Newark, California, USA"

Perform the indicated operations


Solution:

Consider the given equation above


The first that we have to do is to examine the radicals first if they can simplify or not. As a rule in Mathematics, all radicals must be simplified as much as we can. Although the given radical equations are all numbers, then still, we have to follow the principles of Algebra which is "like combines like". 

At the first term, 54 is not a perfect cube. The factors of 54 are 27 and 2. 27 is a perfect cube.

At the second term, 250 is not a perfect cube. The factors of 250 are 125 and 2. 125 is a perfect cube.

At the third term, we need to eliminate the radical sign at the denominator by rationalization of the denominator. Multiply both the numerator and the denominator by 2 so that the denominator becomes a perfect cube which is 8.

Hence, the given equation above becomes







Take the cube root of the numbers inside the radicals that are perfect cube, we have



Since all the terms inside the radicals are the same, then we can combine them and therefore, the final answer is