SOLUTION: Sample answer: It is only necessary to use absolute values when it is possible that n could be odd or even and still be defined. It is when ...

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CCSS PRECISION Simplify.

5.

1.

SOLUTION:

SOLUTION:

ANSWER:

ANSWER: 60x

7.

3.

SOLUTION:

SOLUTION:

ANSWER: 36xy

ANSWER:

9.

SOLUTION:

5.

SOLUTION:

ANSWER: eSolutions Manual - Powered by Cognero

ANSWER:

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ANSWER:

ANSWER: 36xy 6-5 Operations with Radical Expressions

9.

13.

SOLUTION:

SOLUTION:

ANSWER:

ANSWER: 11.

SOLUTION: 15.

SOLUTION:

ANSWER:

13.

SOLUTION:

ANSWER:

17. GEOMETRY Find the altitude of the triangle if the area is square centimeters.

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ANSWER:

Page 2

ANSWER:

ANSWER: cm

6-5 Operations with Radical Expressions

Simplify.

17. GEOMETRY Find the altitude of the triangle if the area is square centimeters.

19.

SOLUTION:

SOLUTION: Let h be the altitude of the triangle.

ANSWER:

21.

Solve for h.

SOLUTION:

Therefore, the altitude of the triangle is

cm.

ANSWER:

ANSWER:

cm

Simplify.

23.

19.

SOLUTION:

SOLUTION:

ANSWER:

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Page 3

ANSWER:

ANSWER:

6-5 Operations with Radical Expressions

27.

23.

SOLUTION:

SOLUTION:

ANSWER: 29.

SOLUTION:

ANSWER:

ANSWER:

31. 25.

SOLUTION:

SOLUTION:

ANSWER:

ANSWER:

33.

SOLUTION:

27.

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SOLUTION:

ANSWER:

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ANSWER:

ANSWER: 2

ft

6-5 Operations with Radical Expressions

Simplify.

33.

SOLUTION:

37.

SOLUTION:

ANSWER:

ANSWER:

35. GEOMETRY Find the area of the rectangle.

39.

SOLUTION: SOLUTION: The area of a rectangle of length l and width w is A = lw.

ANSWER: 1260

Therefore, the area of the rectangle is 2

ft .

41.

ANSWER: 2

ft

SOLUTION:

Simplify.

37.

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ANSWER:

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ANSWER:

ANSWER: 1260 6-5 Operations with Radical Expressions

Simplify.

41.

45.

SOLUTION:

SOLUTION:

ANSWER:

ANSWER:

47.

SOLUTION:

43.

SOLUTION:

ANSWER:

49.

SOLUTION:

ANSWER:

Simplify.

45.

ANSWER:

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Page 6

ANSWER: ANSWER: or

6-5 Operations with Radical Expressions

53.

49.

SOLUTION:

SOLUTION:

ANSWER:

ANSWER:

Simplify each expression if b is an even number.

55.

51.

SOLUTION:

SOLUTION:

ANSWER:

57.

ANSWER:

SOLUTION: or

53.

ANSWER:

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59. MULTIPLE REPRESENTATIONS In this problem, you will explore operations with like radicals.

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an isosceles right triangle with legs of length 2 units.

ANSWER: 6-5 Operations with Radical Expressions

Therefore,

.

d.

59. MULTIPLE REPRESENTATIONS In this problem, you will explore operations with like radicals.

e . The square creates 4 triangles with a base of 1 and a height of 1.

a. NUMERICAL Copy the diagram at the right on dot paper. Use the Pythagorean Theorem to prove that the length of the red segment is units.

b. GRAPHICAL Extend the segment to represent

.

Therefore the area of each triangle is .

The area of the square is 2, so

.

ANSWER:

c. ANALYTICAL Use your drawing to show that

or 2.

d. GRAPHICAL Use the dot paper to draw a units.

square with side lengths

e . NUMERICAL Prove that the area of the square

b.

is

square units.

SOLUTION: a.

c. units is the length of the hypotenuse of an isosceles right triangle with legs of length 2 units. Therefore, .

d.

b.

c. units is the length of the hypotenuse of an isosceles right triangle with legs of length 2 units.

Therefore,

e . The square creates 4 triangles with a base of 1 and a height of 1.

Therefore the area of each triangle is

.

.

d. eSolutions Manual - Powered by Cognero

The area of the square is 2, so

.

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Therefore the area of each triangle is 6-5 Operations with . Radical Expressions

The area of the square is 2, so

.

63. CHALLENGE Find four combinations of whole numbers that satisfy .

61. CHALLENGE Show that

is a cube root

SOLUTION:

of 1.

SOLUTION:

ANSWER:

a = 1, b = 256; a = 2, b = 16; a = 4, b = 4; a = 8, b=2 65. WRITING IN MATH Explain why absolute values may be unnecessary when an nth root of an even power results in an odd power.

ANSWER:

SOLUTION: Sample answer: It is only necessary to use absolute values when it is possible that n could be odd or even and still be defined. It is when the radicand must be nonnegative in order for the root to be defined that the absolute values are not necessary.

ANSWER: Sample answer: It is only necessary to use absolute values when it is possible that n could be odd or even and still be defined. It is when the radicand must be nonnegative in order for the root to be defined that the absolute values are not necessary.

67. When the number of a year is divisible by 4, the year is a leap year. However, when the year is divisible by 100, the year is not a leap year, unless the year is divisible by 400. Which is not a leap year?

63. CHALLENGE Find four combinations of whole numbers that satisfy .

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SOLUTION:

F 1884

G 1900

H 1904

J 1940

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values when it is possible that n could be odd or even and still be defined. It is when the radicand must be nonnegative in order for the root to be defined that the absolute with valuesRadical are not Expressions necessary. 6-5 Operations

ANSWER: G

67. When the number of a year is divisible by 4, the year is a leap year. However, when the year is divisible by 100, the year is not a leap year, unless the year is divisible by 400. Which is not a leap year?

69. SAT/ACT The expression to which of the following?

is equivalent

A

F 1884

B

G 1900

C

H 1904

D

J 1940

E SOLUTION: 1900 is divisible by 100 and 1900 is not divisible by 400. Therefore, 1900 is not a leap year.

SOLUTION:

Option G is the correct answer.

ANSWER: G

69. SAT/ACT The expression to which of the following?

Therefore, option C is the correct answer. ANSWER: C

is equivalent

A

Simplify.

B

C

71.

SOLUTION:

D

E

SOLUTION:

ANSWER: 3

9ab

73. Graph

.

Therefore, option C is the correct answer. ANSWER: eSolutions C Manual - Powered by Cognero

SOLUTION: Graph the inequality

. Page 10

ANSWER: 3

9ab 6-5 Operations with Radical Expressions 73. Graph

Solve each equation.

.

75.

SOLUTION: Graph the inequality

.

SOLUTION:

2

Let y = x .

By the Zero Product Property:

ANSWER:

The solutions are –4, 4,–i and i.

ANSWER: –4, 4, –i, i

77.

SOLUTION:

Solve each equation.

75.

SOLUTION:

By the Zero Product Property:

2

Let y = x .

By the Zero Product Property:

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ANSWER: –4, 4, –i, i 6-5 Operations with Radical Expressions

ANSWER:

79.

77.

SOLUTION:

SOLUTION:

By the Zero Product Property:

By the Zero Product Property:

The solutions are

and

.

ANSWER:

The solutions are

and –4.

ANSWER:

81. CONSTRUCTION Cho charges $1500 to build a small deck and $2500 to build a large deck. During the spring and summer, she built 5 more small decks than large decks. If she earned $23,500 how many of each type of deck did she build?

79.

SOLUTION:

SOLUTION: Let s and l be the number of small and large desk respectively.

The system of equations representing this situation is:

Substitute l + 5 for s in the first equation and solve for l.

By the Zero Product Property:

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ANSWER:

ANSWER: 9 small, 4 large

6-5 Operations with Radical Expressions

81. CONSTRUCTION Cho charges $1500 to build a small deck and $2500 to build a large deck. During the spring and summer, she built 5 more small decks than large decks. If she earned $23,500 how many of each type of deck did she build?

Evaluate each expression.

83.

SOLUTION:

SOLUTION: Let s and l be the number of small and large desk respectively.

The system of equations representing this situation is:

ANSWER:

Substitute l + 5 for s in the first equation and solve for l.

85.

SOLUTION:

Substitute 4 for l in the second equation and solve for s.

s=4+5=9

She built 9 small decks and 4 large decks.

ANSWER: 9 small, 4 large

ANSWER:

Evaluate each expression.

87. 83.

SOLUTION:

SOLUTION:

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ANSWER: 6-5 Operations with Radical Expressions

87.

SOLUTION:

ANSWER:

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Page 14