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Radical Functions — Test Answers

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Which shows the true solution(s) to the radical equation x minus 3 is equal to square root of 4 x minus 7 end root ?

A
x is equal to 2 and x is equal to 8
B
x is equal to 8
C
There are no true solutions to the equation.
D
x is equal to 2
2
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The potential solutions to the radical equation square root of A plus 5 end root is equal to A plus 3 are A is equal to negative 4 and A is equal to negative 1 Which statement is true about these solutions?

A
The solution A is equal to negative 4 is an extraneous solution.
B
Both A is equal to negative 4 and A is equal to negative 1 are true solutions.
C
The solution A is equal to negative 1 is an extraneous solution.
D
Neither A is equal to negative 4 nor A is equal to negative 1 are true solutions.
3

What is the following product? square root of 30 times square root of 10

A
10 square root of 3
B
3 square root of 10
C
2 square root of 10
D
4 square root of 10
4

Which expression is equivalent to the fraction with numerator square root of 10 and denominator 4th root of 8 ?

A
the fraction with numerator 4th root of 200 and denominator 2
B
the fraction with numerator 2 square root of 5 and denominator 5
C
the fraction with numerator 4th root of 20 and denominator 2
D
100 eighths
5

Which expression is equivalent to 4th root of 144 A to the 12th power b cubed ? Assume A is greater than or equal to 0 and b is greater than or equal to 0

A
12 A to the 6th power b open paren 4th root of b close paren
B
2 A to the 4th power b open paren 4th root of 18 close paren
C
2 A cubed open paren 4th root of 9 b cubed close paren
D
12 A cubed open paren 4th root of b cubed close paren
7

What is the solution of square root of x plus 2 end root minus 15 is equal to negative 3 ?

A
x is equal to 142
B
x is equal to 232
C
x is equal to 322
D
no solution
8

What is the solution of square root of x plus 12 end root is equal to x ?

A
x is equal to negative 3
B
x is equal to 4
C
x is equal to negative 3 or x is equal to 4
D
no solution
9

Solve the radical equation x minus 7 is equal to square root of negative 4 x plus 28 end root Which statement is true about the solutions to the radical equation?

A
There are two true solutions.
B
There are no true solutions.
C
There is one extraneous solution, with a value greater than 4 .
D
There is one true solution, with a value greater than 6 .
10

Which function is undefined for x is equal to 0 ?

A
y is equal to cube root of x plus 2
B
y is equal to square root of x minus 2 end root
C
y is equal to square root of x plus 2 end root
D
y is equal to cube root of x minus 2
11

What is the following product? Assume x is greater than or equal to 0 open paren 4 x square root of 5 x squared end root plus 2 x squared square root of 6 close paren squared

A
104 x to the 6th power
B
80 x to the 6th power plus 8 x to the 5th power plus 8 x to the 5th power square root of 30 plus 24 x to the 4th power
C
104 x to the 4th power plus 16 x to the 4th power square root of 30
D
104 x to the 4th power plus 8 x to the 4th power square root of 30 x
13

What is the following quotient? the fraction with numerator 9 plus square root of 2 and denominator 4 minus square root of 7

A
the fraction with numerator 36 minus 9 square root of 7 plus 4 square root of 2 minus square root of 14 and denominator 9
B
the fraction with numerator 9 square root of 7 plus square root of 14 and denominator negative 3
C
79 ninths
D
the fraction with numerator 36 plus 9 square root of 7 plus 4 square root of 2 plus square root of 14 and denominator 9
14

What is the following quotient? the fraction with numerator 1 and denominator 1 plus square root of 3

A
the fraction with numerator 1 minus square root of 3 and denominator 4
B
the fraction with numerator negative 1 plus square root of 3 and denominator 2
C
the fraction with numerator 1 plus square root of 3 and denominator 4
D
the fraction with numerator square root of 3 and denominator 4
15

What is the following sum? 5 x open paren cube root of x squared y close paren plus 2 times open paren cube root of x to the 5th power y close paren

A
7 x open paren 6th root of x squared y close paren
B
7 x open paren cube root of x squared y close paren
C
7 x squared open paren 6th root of x y squared close paren
D
7 x squared open paren cube root of x y squared close paren
16

What is the following product? cube root of 16 x to the 7th power times cube root of 12 x to the 9th power

A
4 x squared open paren cube root of 3 x squared close paren
B
4 x to the 5th power open paren cube root of 3 x close paren
C
x to the 5th power times open paren cube root of 28 x close paren
D
x squared times open paren cube root of 28 x squared close paren
17

If the range of f of x is equal to square root of m x and the range of g of x is equal to m square root of x are the same, which statement is true about the value of m ?

A
m can be any positive real number.
B
m can be any negative real number.
C
m can be any real number.
D
m can only equal 1 .
18

Which of the following is the graph of y is equal to square root of negative x minus 3 end root ?

A
Image with description On a coordinate plane, the x and y axes range from negative 9 to 9 with increments of 1. The curve opens up and to the right in quadrants III and IV. The origin of the curve is negative 3 comma 0. The curve passes through the point 0 comma 1 point 6 and 6 comma negative 3, and end at 9 comma negative 3 point 5. The arrow is present on both end of the curve.
B
Image with description On a coordinate plane x and y axes range from negative 9 to 9 in increments of 1. The curve originates from (3 comma 0) and decreases into the fourth quadrant. It passes through points (4 comma negative 1) and (7 comma negative 2).
C
Image with description On a coordinate plane x and y axes range from negative 9 to 9 in increments of 1. The curve originates from (3 comma 0) and passes through points (negative 1 comma 2) and (negative 6 comma 3) in the 2nd quadrant.
D
Image with description On a coordinate plane x and y axes range from negative 9 to 9 in increments of 1. The curve opens down and to the left in quadrant 2. The origin of the curve is (negative 3 comma 0) and passes through (negative 7 comma 2).
20

What is the simplest form of 4th root of 81 x to the 8th power y to the 5th power ?

A
3 x squared y open paren 4th root of y close paren
B
9 x to the 4th power y squared open paren 4th root of y close paren
C
9 x squared y open paren 4th root of y close paren
D
3 x squared open paren 4th root of y to the 5th power close paren

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