Simplifying Radical ExpressionsA series of free Intermediate Algebra Video Lessons from Brightstorm online Algebra series.
Simplifying Radicals using Rational Exponents When simplifying roots that are either greater than four or have a term raised to a large number, we rewrite the problem using rational exponents. Remember that every root can be written as a fraction, with the denominator indicating the root's power. When simplifying radicals, since a power to a power multiplies the exponents, the problem is simplified by multiplying together all the exponents.
Multiplying Radicals of the Same Root When multiplying radical expressions of the same power, be careful to multiply together only the terms inside the roots and only the terms outside the roots; keep them separate. After multiplying the terms together, we rewrite the root separating perfect squares if possible. The rules of distributing and multiplying binomials (FOIL) apply to radicals as well.
Multiplying Radicals of Different Roots To simplify two radicals with different roots, we first rewrite the roots as rational exponents. Before the terms can be multiplied together, we change the exponents so they have a common denominator. By doing this, the bases now have the same roots and their terms can be multiplied together. Next, we write the problem using root symbols and then simplify.
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