1. 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.
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2. 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
= = 13
= = 7
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3. 243 = 81 • 3 81 is a perfect square and a factor of 243.
Simplifying Radicals
ALGEBRA 1 LESSON 9-3
Simplify
243 = • is a perfect square and a factor of 243.
= • Use the Multiplication Property of Square Roots.
= Simplify
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4. 28x7 = 4x6 • 7x 4x6 is a perfect square and a factor of 28x7.
Simplifying Radicals
ALGEBRA 1 LESSON 9-3
Simplify x7.
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.
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5. Simplify each radical expression.
Simplifying Radicals
ALGEBRA 1 LESSON 9-3
Simplify each radical expression.
a •
12 • = • 32 Use the Multiplication Property of
Square Roots.
= Simplify under the radical.
= • 6 64 is a perfect square and a factor of 384.
= • 6 Use the Multiplication Property of
Square Roots.
= Simplify
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6. 7 5x • 3 8x = 21 40x2 Multiply the whole numbers and
Simplifying Radicals
ALGEBRA 1 LESSON 9-3
(continued)
b x • x
7 5x • x = x2 Multiply the whole numbers and
use the Multiplication Property of
Square Roots.
= x2 • 10 4x2 is a perfect square and a
factor of 40x2.
= x2 • Use the Multiplication Property of
Square Roots.
= 21 • 2x Simplify 4x2.
= 42x Simplify.
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7. 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 = h to estimate the distance you can see to the horizon.
d = h
= • 54 Substitute 54 for h.
= Multiply.
= 9 Simplify
The distance you can see is 9 miles.
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8. 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 13 8
= Use the Division Property of Square Roots. 49 x4 7 x2
= Simplify and x4.
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9. Simplify each radical expression.
Simplifying Radicals
ALGEBRA 1 LESSON 9-3
Simplify each radical expression. a.
120 10
= Divide.
120 10
= 4 • 3 4 is a perfect square and a factor of 12.
= 4 • 3 Use the Multiplication Property of Square Roots.
= Simplify
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10. = 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 , x4, and
5x2 4
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11. 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
3 7 7
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12. 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 x4.
33x
6x2
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13. Simplify each radical expression.
Simplifying Radicals
ALGEBRA 1 LESSON 9-3
Simplify each radical expression. • 12 36 3
8 2 48 2 a5
2 a a3 3x
15x3 5 5x
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