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Prentice Hall Lesson 11.1How do you simplify a radical expression? What is the multiplication property of square roots?

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Possible Answer: The function is linear with a slope of -2 and y-intercept of 7.

Prentice Hall Lesson 11.1How do you simplify a radical expression? What is the multiplication property of square roots?

Toolbox:• Radical expressions contain a radical• Multiplication Property of Square Roots: For every number a ≥ 0 and b ≥ 0, √a•b = √a • √b• To simplify radical expressions, rewrite the radicand as a product of perfect-square factors and the remaining factors. Simplify by taking the square root of the perfect-square factors, leaving the remaining factors as the radicand.

• You may use the product of radicals to find perfect-square factors needed to simplify radical expressions.

• Division Property of Square Roots:For every number a ≥ 0 and b > 0, √ = √a

√b• When the denominator of the radicand is a

perfect square, it is easier to simplify the numerator and denominator separately.

• When the denominator of the radicand is not a perfect square, divide first, then simplify.

• When the radicand in the denominator is not a perfect square, you may need to rationalize the denominator. Multiply the numerator and denominator by the same radical expression, making the denominator a perfect square.

• A radical expression is in simplest radical form when all three statements are true:– The radicand has no perfect-square factors

other than 1.– The radicand has no fractions.– The denominator of a fraction has no radical.

Simplify 243.

ALGEBRA 1 LESSON 11-1ALGEBRA 1 LESSON 11-1

11-1

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.

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.

11-1

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.

11-1

(continued)


b. 7 5x • 3 8x

= 42x 10 Simplify.

= 21 • 2x 10 Simplify 4x2.

= 21 4x2 • 10 Use the Multiplication Property of

Square Roots.

= 21 4x2 • 10 4x2 is a perfect square and a

factor of 40x2.

7 5x • 3 8x = 21 40x2 Multiply the whole numbers and

use the Multiplication Property of

Square Roots.

11-1

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

The distance you can see is 9 miles.

= 9 Simplify 81.

= 81 Multiply.

= 1.5 • 54 Substitute 54 for h.

11-1



= Simplify 64. 13

8

a. 1364

b. 49x4

7

x2 = Simplify 49 and x4.

11-1

= Use the Division Property of Square Roots.1364

13

64

= Use the Division Property of Square Roots.49x4

49

x4


= 12 Divide.120 10

= 4 • 3 4 is a perfect square and a factor of 12.

a. 120 10


= 4 • 3 Use the Multiplication Property of Square Roots.

= 2 3 Simplify 4.

11-1

b. 75x5

48x


= Divide the numerator and denominator by 3x.75x5

48x25x4

16

= Use the Division Property of Square Roots.25x4

16

(continued)

= Use the Multiplication Property ofSquare Roots.

25 • x4

16

= Simplify 25, x4, and 16.5x2

4

11-1

3

7

3

7

7

7 7

7= • Multiply by to make the denominator a

perfect square.



a. 3 7

= Simplify 49.3 7 7

11-1

= Use the Multiplication Property of Square Roots.3 7

49

= Simplify 36x4. 33x

6x2


(continued)

b. 11

12x3

11-1

Simplify the radical expression.

= • Multiply by to make the denominator a

perfect square.

3x

3x

3x

3x

11

12x3

11

12x3

= Use the Multiplication Property of Square Roots. 33x

36x4

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