Complete each equation. 1. a 3 = a2 • a 2. b 7 = b6 • b Simplifying Radicals ALGEBRA 1 LESSON 9-3 Complete each equation. 1. a 3 = a2 • a 2. b 7 = b6 • b 3. c 6 = c3 • c 4. d 8 = d4 • d Find the value of each expression. 5. 4 6. 169 7. 25 8. 49 9-3

1. a3 = a(2 + 1) = a2 • a1 2. b7 = b(6 + 1) = b6 • b1 Simplifying Radicals ALGEBRA 1 LESSON 9-3 Solutions 1. a3 = a(2 + 1) = a2 • a1 2. b7 = b(6 + 1) = b6 • b1 3. c6 = c(3 + 3) = c3 • c3 4. d8 = d(4 + 4) = d4 • d4 5. 4 = 2 6. 169 = 13 7. 25 = 5 8. 49 = 7 9-3

243 = 81 • 3 81 is a perfect square and a factor of 243. Simplifying Radicals ALGEBRA 1 LESSON 9-3 Simplify 243. 243 = 81 • 3 81 is a perfect square and a factor of 243. = 81 • 3 Use the Multiplication Property of Square Roots. = 9 3 Simplify 81. 9-3

28x7 = 4x6 • 7x 4x6 is a perfect square and a factor of 28x7. Simplifying Radicals ALGEBRA 1 LESSON 9-3 Simplify 28x7. 28x7 = 4x6 • 7x 4x6 is a perfect square and a factor of 28x7. = 4x6 • 7x Use the Multiplication Property of Square Roots. = 2x3 7x Simplify 4x6. 9-3

Simplify each radical expression. Simplifying Radicals ALGEBRA 1 LESSON 9-3 Simplify each radical expression. a. 12 • 32 12 • 32 = 12 • 32 Use the Multiplication Property of Square Roots. = 384 Simplify under the radical. = 64 • 6 64 is a perfect square and a factor of 384. = 64 • 6 Use the Multiplication Property of Square Roots. = 8 6 Simplify 64. 9-3

7 5x • 3 8x = 21 40x2 Multiply the whole numbers and Simplifying Radicals ALGEBRA 1 LESSON 9-3 (continued) b. 7 5x • 3 8x 7 5x • 3 8x = 21 40x2 Multiply the whole numbers and use the Multiplication Property of Square Roots. = 21 4x2 • 10 4x2 is a perfect square and a factor of 40x2. = 21 4x2 • 10 Use the Multiplication Property of Square Roots. = 21 • 2x 10 Simplify 4x2. = 42x 10 Simplify. 9-3

The distance you can see is 9 miles. Simplifying Radicals ALGEBRA 1 LESSON 9-3 Suppose you are looking out a fourth floor window 54 ft above the ground. Use the formula d = 1.5h to estimate the distance you can see to the horizon. d = 1.5h = 1.5 • 54 Substitute 54 for h. = 81 Multiply. = 9 Simplify 81. The distance you can see is 9 miles. 9-3

Simplify each radical expression. Simplifying Radicals ALGEBRA 1 LESSON 9-3 Simplify each radical expression. a. 13 64 b. 49 x4 = Use the Division Property of Square Roots. 13 64 = Simplify 64. 13 8 = Use the Division Property of Square Roots. 49 x4 7 x2 = Simplify 49 and x4. 9-3

Simplify each radical expression. Simplifying Radicals ALGEBRA 1 LESSON 9-3 Simplify each radical expression. a. 120 10 = 12 Divide. 120 10 = 4 • 3 4 is a perfect square and a factor of 12. = 4 • 3 Use the Multiplication Property of Square Roots. = 2 3 Simplify 4. 9-3

= Divide the numerator and denominator by 3x. Simplifying Radicals ALGEBRA 1 LESSON 9-3 (continued) b. 75x5 48x = Divide the numerator and denominator by 3x. 75x5 48x 25x4 16 = Use the Division Property of Square Roots. 25x4 16 = Use the Multiplication Property of Square Roots. 25 • x4 16 = Simplify 25, x4, and 16. 5x2 4 9-3

Simplify each radical expression. Simplifying Radicals ALGEBRA 1 LESSON 9-3 Simplify each radical expression. a. 3 7 3 7 = • Multiply by to make the denominator a perfect square. = Use the Multiplication Property of Square Roots. 3 7 49 = Simplify 49. 3 7 7 9-3

Simplify the radical expression. Simplifying Radicals ALGEBRA 1 LESSON 9-3 (continued) Simplify the radical expression. b. 11 12x3 = • Multiply by to make the denominator a perfect square. 3x 11 12x3 = Use the Multiplication Property of Square Roots. 33x 36x4 = Simplify 36x4. 33x 6x2 9-3

Simplify each radical expression. Simplifying Radicals ALGEBRA 1 LESSON 9-3 Simplify each radical expression. 1. 16 • 8 2. 4 144 3. 4. 5. 12 36 3 8 2 48 2 a5 2 a a3 3x 15x3 5 5x 9-3