Dividing Radicals using Conjugates
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This document provides instructions for dividing radicals and rationalizing denominators. It discusses simplifying coefficients and radicands when dividing radicals. When rationalizing denominators, it explains multiplying the numerator and denominator by a radical term called the conjugate to eliminate radicals in the denominator. The conjugate is formed by changing the sign of the second term of a binomial. Examples are provided to demonstrate rationalizing denominators using conjugates.
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Dividing Radicals using Conjugates
- 2. DIVIDING RADICALS 1) Simplify any coefficients 2) Simplify the radicands, if possible 3) Rationalize if necessary
- 3. REVIEW RATIONALIZING Rationalizing the denominator is a process by which is fraction is rewritten so that the denominator only contains rational numbers (no radicals). Create an equivalent fraction by multiplying the numerator and denominator by a radical; create a perfect root in the denominator
- 4. PRACTICE
- 5. WHAT IF THERE IS MORE THAN ONE TERM IN THE DENOMINATOR?
- 6. RATIONALIZING USING A CONJUGATE In algebra, the conjugate is a binomial formed by negating the second term of a binomial. For example: the conjugate of (x+y) is (x-y), when x and y are Real numbers If the numbers are imaginary, the process is called complex conjugation The complex conjugate of (a+bi) is (a-bi), where a and b are Real and “i” is the imaginary number.
- 7. RATIONALIZING USING A CONJUGATE The conjugate of a denominator is the same expression but with a different sign in the middle. This will allow terms with a radical to eliminate because of inverse operations
- 8. RATIONALIZING USING A CONJUGATE 1) Find the conjugate of the denominator 2) Multiply the numerator and denominator by the conjugate (you will have to FOIL the denominators) 3) Simplify!
- 10. PRACTICE