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Rationalizing Denominators and Numerators of Radical Expressions

Rationalizing Denominators and Numerators of Radical Expressions. Section 8.5. DMA 080. Simplified Form of a Radical Expression. Each factor in the radicand is to a power that is less than the index of the radical The radicand contains no fractions or negative numbers

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Rationalizing Denominators and Numerators of Radical Expressions

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  1. Rationalizing Denominators and Numerators of Radical Expressions Section 8.5 DMA 080

  2. Simplified Form of a Radical Expression • Each factor in the radicand is to a power that is less than the index of the radical • The radicand contains no fractions or negative numbers • No radicals appear in the denominator of a fraction

  3. Rationalizing Denominators • To rationalize a square root denominator, multiply the numerator and denominator of the given fraction by the square root that makes a perfect square radicand in the denominator.

  4. Rationalizing the Denominator • Given is this simplified? We need to find a fraction that is equivalent that does not have a radical in the denominator.

  5. The Language of Algebra • Since is an irrational number, has an irrational denominator. • Since is a rational number, has a rational denominator.

  6. Example • Rationalize the denominator:

  7. Rationalizing Denominators • To rationalize a cube root denominator, multiply the numerator and denominator of the given fraction by the cube root that makes a perfect-cube radicand in the denominator.

  8. Example • Rationalize the denominator

  9. Example • Rationalize the denominator:

  10. Example • Rationalize the denominator:

  11. Example • Rationalize each denominator:

  12. Rationalizing Denominators with 2 Terms • Two-termed denominators To rationalize, multiply numerator and denominator by To rationalize, multiply the numerator and denominator by Radical expressions that involve the sum and difference of the same two terms such as are called conjugates.

  13. Example • Rationalize the denominator:

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