prentice hall lesson 11.1 how do you simplify a radical expression? what is the multiplication...
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Prentice Hall Lesson 11.1How do you simplify a radical expression? What is the multiplication property of square roots?
BOP:
Solution to BOP:
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.
ALGEBRA 1 LESSON 11-1ALGEBRA 1 LESSON 11-1
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.
ALGEBRA 1 LESSON 11-1ALGEBRA 1 LESSON 11-1
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)
ALGEBRA 1 LESSON 11-1ALGEBRA 1 LESSON 11-1
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.
ALGEBRA 1 LESSON 11-1ALGEBRA 1 LESSON 11-1
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 each radical expression.
ALGEBRA 1 LESSON 11-1ALGEBRA 1 LESSON 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
ALGEBRA 1 LESSON 11-1ALGEBRA 1 LESSON 11-1
= 12 Divide.120 10
= 4 • 3 4 is a perfect square and a factor of 12.
a. 120 10
Simplify each radical expression.
= 4 • 3 Use the Multiplication Property of Square Roots.
= 2 3 Simplify 4.
11-1
b. 75x5
48x
ALGEBRA 1 LESSON 11-1ALGEBRA 1 LESSON 11-1
= 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.
ALGEBRA 1 LESSON 11-1ALGEBRA 1 LESSON 11-1
Simplify each radical expression.
a. 3 7
= Simplify 49.3 7 7
11-1
= Use the Multiplication Property of Square Roots.3 7
49
= Simplify 36x4. 33x
6x2
ALGEBRA 1 LESSON 11-1ALGEBRA 1 LESSON 11-1
(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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