Question : The process of eliminating the radical in the denominator of a radical expression : 2163589

MULTIPLE CHOICE. Choose the one alternative that best completes the statement or answers the question.

Fill in the blank with one of the words or phrases listed below. Not all the choices will be used.

1) The expression 5√(x) and 7√(x) are examples of _______.

A) conjugate

B) principal square root

C) rationalizing the denominator

D) like radicals

2) In the expression 3√(45) the number 3 is the _______, the number 45 is the _______, and √( ) is called the _______ sign.

A) radical, radicand, index

B) radicand, radical, index

C) index, radical, radicand

D) index, radicand, radical

3) The _______ of a + b is a - b.

A) conjugate

B) radicand

C) radical

D) principal square root

4) The _______ of 25 is 5.

A) conjugate

B) radical

C) principal square root

D) radicand

5) The process of eliminating the radical in the denominator of a radical expression is called _______.

A) rationalizing the denominator

B) radicand

C) principal square root

D) conjugate

6) The Pythagorean theorem states that (leg)² + (leg)² = (_______)².

A) leg

B) radical

C) index

D) hypotenuse

Simplify the radical. Indicate if the radical is not a real number. Assume that x represents a positive real number.

7) √(64)

A) Not a real number

B) -8

C) 8

D) 32

8) 3√(8)

A) 4

B) 2

C) 3

D) ±2

9) 4√(256)

A) 6.233

B) 4

C) 16

D) Not real number

10) √((25/49))

A) (5/7)

B) (5/8)

C) (6/7)

D) (1/2)

11) 4√(-625)

A) Not real number

B) 25

C) 5

D) -5

12) √(x⁶)

A) x³

B) 3√(x)

C) x^√(6)

D) x⁶

Simplify the radical. Assume that all variables represent positive numbers.

13) √(72)

A) 6√(2)

B) 12

C) 2√(6)

D) 8

14) √(2541)

A) 33√(7)

B) 11√(21)

C) 121√(21)

D) 77√(3)

15) √(y¹¹)

A) √(y¹¹)

B) y⁵√(y)

C) y¹⁰√(y)

D) y√(y⁹)

16) √(252y²)

A) 6√(7y²)

B) 6y2√(7)

C) 6√(7)

D) 6y√(7)

17) 3√(-1000)

A) 100

B) ±10

C) 32

D) -10

18) 3√(108)

A) 3

B) 3√3(12)

C) 3√3(4)

D) 12

19) √((7/36))

A) (√(7)/6)

B) (7/6)

C) √((7/36))

D) (√(7)/36)

20) √((x⁷/16))

A) (x³x/4)

B) (x√(x⁵)/4)

C) (x³√(x)/4)

D) (√(x⁷)/4)

Perform the indicated operation. Assume that all variables represent positive numbers.

21) 12√(7) - 8√(7) - √(7)

A) 3√(7)

B) 5√(7)

C) 4√(7)

D) -5√(7)

22) √(300) + √(720) + √(192) + 4√(20)

A) 164√(3) + 160√(5)

B) 38√(8)

C) 18√(3) + 14√(5)

D) 18√(3) + 20√(5)

23) √((6/16)) + √((150/9))

A) (23√(6)/4)

B) (23√(6)/12)

C) (5/2)

D) (-17√(6)/12)

24) √(5)⋅√(15)

A) 15

B) √(75)

C) 5√(3)

D) 5

25) √(7)(√(14) - √(7))

A) 14 - 49

B) 7√(2) - 7

C) 7√(2) - 49

D) 49√(2) - 7

26) (7√(x) + 6 )(√(x) - 2)

A) 7x - 8√(x) + 12

B) 7x - 8√(x) - 12

C) 7x + 8√(x) - 12

D) 7x + 20√(x) - 12

27) (√(100)/√(5))

A) (√(500)/5)

B) 5

C) (√(100)/5)

D) 2√(5)

28) (√(810x¹¹)/√(5x⁹))

A) 9x¹⁰√(2)

B) 9x√(2)

C) x√(162)

D) 9x√(10)

Rationalize the denominator and simplify. Assume that all variables represent positive real numbers.

29) √((7/5))

A) (√(35)/5)

B) √(35)

C) √(7)

D) (√(35)/25)

30) (3/√(2p))

A) 7p

B) 3√(2p)

C) (3√(2p)/2p)

D) (9√(2p)/2p)

31) (4/√(10) + 3)

A) 4√(10) + 12

B) 4√(10) - 3

C) (4√(10) + 12/20)

D) 4√(10) - 12

32) (7√(2)/√(x) - 9)

A) (7√(2x) + 63√(2)/x - 9)

B) (7√(2x) + 63√(2)/x - 81)

C) (7√(2x) - 63√(2)/x + 81)

D) (7√(2x) - 63√(2)/x - 9)

Solve the equation.

33) √(x) + 8 = 9

A) 1

B) -1

C) 289

D) No solution

34) √(2x - 5) = √(x + 7)

A) 6

B) 2

C) (2/3)

D) 12

35) √(20x - 60) = x + 2

A) 7

B) 8

C) -7

D) -8

Solve the problem.

36) Find the length of the unknown leg of the right triangle shown. Give an exact answer.

15 inches

9 inches

A) 12 in.

B) in.14

C) 15 in.

D) 11 in.

37) The formula v = √(2.5r) can be used to estimate the maximum safe velocity v, in miles per hour, at which a car can travel along a curved road with a radius of curvature r, in feet. To the nearest whole number, find the maximum safe speed for a curve in a road with a radius of curvature of 150 feet.

A) 12 mph

B) 31 mph

C) 8 mph

D) 19 mph