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Saturday, June 15, 2013

Simplifying Radicals, 3

Category: Algebra

"Published in Newark, California, USA"

Simplify


Solution:

Consider the given equation above


As you noticed that the numerator has a negative sign. Well, it's fine because the cube root of any negative number is always a negative number. Also, the numerator is not a perfect cube because the exponent of x is not a multiple of 3. We need to factor and rewrite x into a multiple of 3 as follows


Take the cube root of the terms with exponents that are multiples of 3, we have


Next, we need to rationalize the denominator in order to eliminate the radical sign at the denominator by multiplying both the numerator and denominator by 22, we have 




Since the exponents of 2 and x are smaller than the index of a radical, therefore the final answer is