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Section 9.3 Multiplying and Dividing Radical Expressions

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9.3 Lecture Guide: Multiplying and Dividing Radical Expressions Objective: Multiply radical expressions.

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To multiply and divide some radical expressions, we use the properties: Multiplying Radicals forand for and

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Perform each indicated multiplication, and then simplify the product. Assume x > 0 and y > 0. 1.

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Perform each indicated multiplication, and then simplify the product. Assume x > 0 and y > 0. 2.

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Perform each indicated multiplication, and then simplify the product. Assume x > 0 and y > 0. 3.

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Perform each indicated multiplication, and then simplify the product. Assume x > 0 and y > 0. 4.

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Perform each indicated multiplication, and then simplify the product. Assume x > 0 and y > 0. 5.

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Perform each indicated multiplication, and then simplify the product. Assume x > 0 and y > 0. 6.

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Perform each indicated multiplication, and then simplify the product. Assume x > 0 and y > 0. 7.

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Perform each indicated multiplication, and then simplify the product. Assume x > 0 and y > 0. 8.

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Simplify each expression. Assume x > 0 and y > 0. 9.

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Simplify each expression. Assume x > 0 and y > 0. 10.

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Simplify each expression. Assume x > 0 and y > 0. 11.

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Simplify each expression. Assume x > 0 and y > 0. 12.

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Objective: Divide and simplify radical expressions.

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Dividing Radicals When dividing radical expressions, we do not always get a result that is rational. In this case, answers are typically given without any radicals in the denominator. Recall that = ____________ for In general, _____________ for

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As a warm-up to rationalizing the denominator of a radical expression, perform each multiplication. 13.

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As a warm-up to rationalizing the denominator of a radical expression, perform each multiplication. 14.

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As a warm-up to rationalizing the denominator of a radical expression, perform each multiplication. 15.

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As a warm-up to rationalizing the denominator of a radical expression, perform each multiplication. 16.

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Perform each division, and then express the quotient in rationalized form. Assume x > 0 and y > 0. 17.

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Perform each division, and then express the quotient in rationalized form. Assume x > 0 and y > 0. 18.

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Perform each division, and then express the quotient in rationalized form. Assume x > 0 and y > 0. 19.

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Perform each division, and then express the quotient in rationalized form. Assume x > 0 and y > 0. 20.

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Perform each division, and then express the quotient in rationalized form. Assume x > 0 and y > 0. 21.

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Perform each division, and then express the quotient in rationalized form. Assume x > 0 and y > 0. 22.

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Conjugates Radicals: The conjugate ofis

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Write the conjugate of each expression. Then multiply the expression by its conjugate. ExpressionConjugateProduct 23. 24. 25. Example:

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Perform the indicated divisions by rationalizing the denominator and then simplifying. Assume that all variables represent positive real numbers. 26.

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Perform the indicated divisions by rationalizing the denominator and then simplifying. Assume that all variables represent positive real numbers. 27.

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Perform the indicated divisions by rationalizing the denominator and then simplifying. Assume that all variables represent positive real numbers. 28.

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Perform the indicated divisions by rationalizing the denominator and then simplifying. Assume that all variables represent positive real numbers. 29.

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Perform the indicated divisions by rationalizing the denominator and then simplifying. Assume that all variables represent positive real numbers. 30.

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Perform the indicated divisions by rationalizing the denominator and then simplifying. Assume that all variables represent positive real numbers. 31.

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Determine whether or not each value of x is a solution of the equation 32.

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Determine whether or not each value of x is a solution of the equation 33.

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Determine whether or not each value of x is a solution of the equation 34.

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Determine whether or not each value of x is a solution of the equation 35.

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