1. Prentice Hall Lesson 11. 1 How do you simplify a radical expression
Prentice Hall Lesson 11.1 How do you simplify a radical expression? What is the multiplication property of square roots? BOP:

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

3. Prentice Hall Lesson 11. 1 How do you simplify a radical expression
Prentice Hall Lesson 11.1 How 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.

4. 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.

5. 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.

6. = 81 • 3 Use the Multiplication Property of Square Roots.
ALGEBRA 1 LESSON 11-1
Simplify
243 = • 3 81 is a perfect square and a factor of 243.
= • 3 Use the Multiplication Property of Square Roots.
= Simplify 81.
11-1

7. = 4x6 • 7x Use the Multiplication Property of Square Roots.
ALGEBRA 1 LESSON 11-1
Simplify x7.
28x7 = 4x6 • 7x 4x6 is a perfect square and a factor of 28x7.
= 4x6 • 7x Use the Multiplication Property of Square Roots.
= 2x x Simplify x6.
11-1

8. Simplify each radical expression.
ALGEBRA 1 LESSON 11-1
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
11-1

9. 7 5x • 3 8x = 21 40x2 Multiply the whole numbers and
ALGEBRA 1 LESSON 11-1
(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.
11-1

10. The distance you can see is 9 miles.
ALGEBRA 1 LESSON 11-1
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.
11-1

11. Simplify each radical expression.
ALGEBRA 1 LESSON 11-1
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.
11-1

12. Simplify each radical expression.
ALGEBRA 1 LESSON 11-1
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
11-1

13. = Divide the numerator and denominator by 3x.
ALGEBRA 1 LESSON 11-1
(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
11-1

14. Simplify each radical expression.
ALGEBRA 1 LESSON 11-1
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
11-1

15. Simplify the radical expression.
ALGEBRA 1 LESSON 11-1
(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
11-1

16. Summary:
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