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By H. Araki, R. V. Kadison

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If the result is a terminating decimal or repeating decimal, the number is rational. If the decimal does not terminate or repeat, it is irrational. Example Is the expression a rational or irrational? ___ ___ a. √81 b. √10 ___ a. √81 = 9 is a perfect square. root sign. Ask if the number is a perfect So the 81 is rational. ___ square. b. √10 is not a perfect square. Step 1 Look at the number under the square ___ Step 2 Find the square root. b. 16227766 Step 3 Look at the result. If the result is a b.

Look at the number outside the symbol to determine the root to calculate. 2. If the number under the symbol is a perfect power, find the root. 3. If the number under the symbol is not a perfect power, find a perfect power less than the number. 4. Then find a perfect power greater than the number. 5. The estimated root is between the two perfect roots. Example 3 __ Find the root: √8 3 __ Step 1 Look at the number outside the symbol √ 8 —determine the root to calculate. Step 2 Determine if the number under the symbol is a perfect power.

4x)(2x2) = 8x3 (4x)(x) = 4x2 (4x)(−6) = −24x 8x3 + 4x2 − 24x Practice Multiply. 1. 3x3(4x2 + 2x − 1) Multiply each term in the polynomial by the monomial. (3x3)(4x2) = (3x3)(2x) = (3x3)(−1) = 2. 7x2(−3x3 + 2) 3. –2x4 (−4x2 + x − 3) 4. x2(3x5 + 6x3 + x) 5. com Name Date Factoring a Binomial By applying the Distributive Property in reverse, you can factor out a common factor. 20 + 15 = (5 × 4) + (5 × 3) = 5 (4 + 3) Rules for Factoring Out the Greatest Common Factor: Factoring Binomials 1. Find the greatest common factor of all the terms.

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