prentice hall lesson 11.4 what are like radicals? how do you combine like radicals? bop:

Prentice Hall Lesson 11.4What are like radicals? How do you combine like radicals?

BOP:

Solution to BOP:

20.DE 6.1; EF 3.6; DF 5.7

22.MN 5.1; NP 3.6; MP = 5

24.TU 7.6; UV 16.5; VT 13.3

26.a. (20, 80), (–40, 30)

b. 78.1 ft

c. (–10, 55) or 55L10

ALGEBRA 1 LESSON 11-3ALGEBRA 1 LESSON 11-3

pages 594–597 Exercises

2. 14

4. 11.3

6. 8.1

8. 21.6

10. (–1, 12)

12. (–2, 3)

14. – 2 , –1

16. 8 , –9

18.9.411-3

12

12


30.about 9.5 km apart

32.Yes; all sides are congruent.

11-3

34.a. about 4.3 mib. about 17.4 mi

Prentice Hall Lesson 11.4What are like radicals? How do you combine like radicals?

Toolbox:• Like radicals in a radical expression have the same radicand.• Unlike radicals do not have the same radicand.• To simplify sums and differences, use the Multiplication Property of Square Roots to simplify the radical expression(s) as needed. Then use the Distributive Property to combine like radicals and simplify.

• To simplify products, use the Distributive Property to multiply. (You may use FOIL if both expressions have two terms.) Combine like radicals and simplify.• Conjugates are the sum and difference of the same two terms.• The product of two conjugates is a difference of two squares.•To simplify a quotient, multiply the numerator and denominator by the conjugate of the denominator. Continue to simplify until the resulting expression meets the three requirements for a radical expression in simplest form.

• A radical expression is in simplest form when it meets the following requirements:1. The radicand has no perfect-square factors

other than 1.

2. The radicand has no fractions.

3. The denominator of a fraction has no radical.

Simplify 4 3 + 3.


= (4 + 1) 3 Use the Distributive Property to combine like radicals.

= 5 3 Simplify.

11-4

4 3 + 3 = 4 3 + 1 3 Both terms contain 3.

8 5 – 45 = 8 5 + 9 • 5 9 is a perfect square and a factor of 45.

Simplify 8 5 – 45.


= 8 5 – 9 • 5 Use the Multiplication Property of Square Roots.

= 8 5 – 3 5 Simplify 9.

= (8 – 3) 5 Use the Distributive Property tocombine like terms.

= 5 5 Simplify.

11-4

Simplify 5( 8 + 9).


5( 8 + 9) = 40 + 9 5 Use the Distributive Property.

= 4 • 10 + 9 5 Use the Multiplication Property of Square Roots.

= 2 10 + 9 5 Simplify.

11-4

Simplify ( 6 – 3 21)( 6 + 21).


( 6 – 3 21)( 6 + 21)

= 36 + 126 – 3 126 – 3 441 Use

FOIL.= 6 – 2 126 – 3(21) Combine like radicals and

simplify 36 and 441.

= 6 – 2 9 • 14 – 63 9 is a perfect square factor of 126.

= 6 – 2 9 • 14 – 63 Use the Multiplication Property of Square Roots.

= 6 – 6 14 – 63 Simplify 9.

= –57 – 6 14 Simplify.

11-4


= 2( 7 + 3) Divide 8 and 4 by the common factor 4.

= 2 7 + 2 3 Simplify the expression.

= Multiply in the denominator. 8( 7 + 3)

7 – 3

= Simplify the denominator. 8( 7 + 3)

4

11-4

Simplify . 8

7 – 3

= • Multiply the numerator and denominator by the conjugate of the denominator.

8

7 – 3

7 + 3

7 + 3

A painting has a length : width ratio approximately equal to the

golden ratio (1 + 5) : 2. The length of the painting is 51 in. Find the

exact width of the painting in simplest radical form. Then find the

approximate width to the nearest inch.


11-4

Define: 51 = length of painting x = width of painting

Relate: (1 + 5) : 2 = length : width

Write: =

x (1 + 5) = 102 Cross multiply.

= Solve for x. 102

(1 + 5)

x(1 + 5)

(1 + 5)

51 x

(1 + 5) 2


(continued)

x = Multiply in the denominator.102(1 – 5) 1 – 5

x = Simplify the denominator.102(1 – 5) –4

x = Divide 102 and –4 by the common factor –2.

– 51(1 – 5) 2

x = 31.51973343 Use a calculator.

x 32The exact width of the painting is inches.

The approximate width of the painting is 32 inches.

– 51(1 – 5) 2

11-4

x = • Multiply the numerator and the denominator by the conjugate of the denominator.

(1 – 5)

(1 – 5) 102

(1 + 5)

16

5 – 7

Simplify each expression.

1. 12 16 – 2 16 2. 20 – 4 5 3. 2( 2 + 3 3)

4. ( 3 – 2 21)( 3 + 3 21) 5.


40 –2 5 2 + 3 6

–123 + 3 7 –8 5 – 8 7

11-4

Summary:

Don’t forget to write your minimum three sentence summary answering today’s essential question here!

prentice hall lesson 11.4 what are like radicals? how do you combine like radicals? bop:

Documents