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Friday, July 5, 2013

Algebraic Operations - Radicals, 20

Category: Algebra, Arithmetic

"Published in Newark, California, USA"

Perform the indicated operations


Consider the given equation above

The above equation can be written as

If you will multiply a radical with another radical with the same index, then the terms inside the radicals will be multiplied together.

As a rule in Mathematics, all radicals in the denominator should be rationalized or eliminated. In this case, multiply both the numerator and the denominator by its conjugate which is 2√2 + 1 so that the radical sign in the denominator will be eliminated as follows

As you notice that the factors in the denominator are the sum and the difference of two squares. Because of the middle term is zero, then there will be no radicals left in the denominator. Although the above equation are all numerals, then we need to apply the principles of Algebra so that the radicals will be rationalize or eliminated as follows

Therefore, the final answer is