To rationalize the denominator of (3)/(√(5)-2), multiply the numerator and denominator by .

Name: Problem 5, Chapter 3: College Algebra
Uploaded: 2023-02-17T19:58:46-08:00
Duration: 1 min 39 s
Channel: Jennifer Stoner
Description: To rationalize the denominator of (3)/(√(5)-2), multiply the numerator and denominator by .

step 1 To rationalize the denominator of 3 over the square of 5 minus 2, we're going to multiply both t

To rationalize the denominator of (3)/(√(5)-2), multiply the...

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Key Concepts

Rationalizing the Denominator

Rationalizing the denominator is a method used in algebra to eliminate irrational numbers (such as square roots) from the denominator of a fraction. This technique simplifies further arithmetic operations and provides a standard form for expressing the result, ensuring that all radicals, when possible, are confined to the numerator.

Conjugate

The conjugate of an expression involving two terms, especially when at least one term is irrational, is formed by changing the sign between the terms. When the original denominator is of the form (a - b) where b is irrational, multiplying the numerator and denominator by (a + b) yields a product that eliminates the radical in the denominator due to the application of the difference of squares.

Difference of Squares

The difference of squares is an algebraic identity defined by the formula (a + b)(a - b) = a² - b². This formula is integral to the process of rationalizing denominators since it allows for the conversion of an expression with radicals into a rational expression by effectively canceling out the irrational parts within the denominator.

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