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Sunday, June 30, 2013

Algebraic Operations - Radicals, 15

Category: Algebra

"Published in Newark, California, USA"

Perform the indicated operations


Solution:

Consider the given equation above


If you will cube a radical in which the index is 2 or that have a square root sign, then the terms inside the square root sign will be raised to a third power. 

If you will multiply a radical with another radical with the same index, then the terms inside the radicals will be multiplied together. In this case, the given above equation can be written as follows 



Apply the principles of Binomial Theorem or squaring of a binomial to the above equation as follows





At the first term, x3 is not a perfect square, the factors of x3 are x2 and x. x2 is a perfect square. 

At the second term, x2 is a perfect square. The square root of x2 is x. 

At the third term, 4y2 is a perfect square. The square root of 4y2 is 2y. 

At the fourth term, 8y3 is not a perfect square, the factors of 8y3 are 4y2 and 2y. 4y2 is a perfect square. 

Hence, the given equation above becomes





Therefore, the final answer is