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Adding, Subtracting, and Multiplying Radical Expressions

Adding, Subtracting, and Multiplying Radical Expressions. Section 8.4 MATH 171-460 Mr. Keltner. Adding & Subtracting Like Radicals. Recall that terms such as 8 x 2 and -5 x 2 are considered like terms because they have identical variable parts.

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Adding, Subtracting, and Multiplying Radical Expressions

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  1. Adding, Subtracting, and Multiplying Radical Expressions Section 8.4 MATH 171-460 Mr. Keltner

  2. Adding & Subtracting Like Radicals • Recall that terms such as 8x2 and -5x2 are considered like terms because they have identical variable parts. • When we combine like terms, we simply combine their coefficients, such as 8x2 + (-5x2) = 3x2. • Like radicals are ones that have the same index and radicand. • Example: and are like radicals.

  3. Example 1:Simplifying Like Radicals • Simplify.

  4. Un-Like Radicals: What to do? • If radicals do not happen to be like radicals, try simplifying each radical term first. • It may just work out that the radicals had more in common than it first appeared.

  5. Example 2: Simplifying Un-Like Radicals • Simplify, assuming all variables represent nonnegative values.

  6. Simplifying using other strategies • We can also simplify radical expressions by: • Using the Distributive Property • Multiplying a conjugate pair (quantities that are the same except for the sign between terms, such as (8-√3) and (8+√3). • Squaring a binomial in the form (a + b)2 • FOIL-ing a pair of binomials

  7. Example 3:Multiplying Expressions • Multiply each expression and simplify.

  8. Expressions with Mixed Operations • In some instances, it may be necessary to simplify an expression with any combination of addition, subtraction, multiplication, and division. • It is best to simplify using the Product and Quotient properties first. • Example 4: Simplify the expression:

  9. Assessment Pgs. 572 - 575: #’s 7 - 98, multiples of 7

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