Rationalize the denominator. (a) (1)/(√(9)) (b) √((25)/(128)) (c) (6)/(√(27 a))

Name: Problem 269, Chapter 8: Intermediate Algebra
Uploaded: 2022-09-29T18:34:24-08:00
Channel: Nicole Hoffman
Description: Rationalize the denominator. (a) (1)/(√(9)) (b) √((25)/(128)) (c) (6)/(√(27 a))

step 1 So this question wants me to rationalize the denominator. So I'm going to get 1 over the 4th roo

Rationalize the denominator. (a) (1)/(√(9)) (b)...

Key Concepts

Rationalizing Denominators

This concept involves rewriting a fraction so that there are no radicals in the denominator. It is achieved by multiplying the numerator and denominator by a form of 1 that will eliminate the irrational part, thereby making the expression easier to work with in further calculations.

Radical Expressions and Rational Exponents

Radicals, such as square roots, fourth roots, or nth roots, can be expressed using fractional exponents. This translation allows the use of exponent rules for simplifying and manipulating expressions, which is especially useful when combining and comparing radical expressions.

Multiplying by an Appropriate Factor

To remove radicals from the denominator, one identifies and multiplies by a factor that, when combined with the existing radical, results in a power that is a whole number under the radical. This method ensures the denominator becomes rational by creating a perfect power, eliminating any irrational parts.

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