radical equations practice 7 multiple choice questions algebra homework help

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Which of the following shows the correct next step when solving the equation below.

square root of t space plus thin space 21 end root space minus space 1 space equals space square root of t space plus space 2 end root
left parenthesis square root of t space plus space 21 end root space minus space 1 right parenthesis squared space equals space left parenthesis square root of t space plus thin space 2 end root right parenthesis squared
A. t space plus space 21 space plus space 1 space plus thin space t space plus space 2
B. t space plus space 21 space minus space 2 square root of t space plus thin space 21 end root space plus space 1 space equals space t space plus space 2
C. t space plus thin space 21 space minus space 2 square root of t space plus thin space 21 end root space plus space 1 space equals space t squared space plus space 4 t space plus thin space 4
D. t space plus thin space 21 space minus space 2 square root of t space plus space 21 end root space minus space 1 space equals space t space plus thin space 2

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Which of the following shows the correct next step when solving the equation below?

left parenthesis 5 x space plus space 7 right parenthesis to the power of 1 third end exponent space plus space 3 space equals space 5
left parenthesis 5 x space plus space 7 right parenthesis to the power of 1 third end exponent space equals space 2
A. 3 root of left parenthesis 5 x space plus space 7 right parenthesis to the power of 1 third end exponent space end root space equals space 3 root of 2
B. left parenthesis left parenthesis 5 x space plus space 7 right parenthesis to the power of 1 third end exponent right parenthesis to the power of 1 third end exponent space equals space 2 to the power of 1 third end exponent
C. square root of left parenthesis 5 x space plus space 7 right parenthesis to the power of 1 third end exponent end root space equals space square root of 2
D. left parenthesis left parenthesis 5 x space plus space 7 right parenthesis to the power of 1 third end exponent right parenthesis cubed space equals space 2 cubed

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Solve the equation for m.

m to the power of 1 third end exponent space plus space 8 space equals space 10


m = 2

m = 8

m = 5832

m = 1

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Solve the equation for t.

t to the power of 1 half end exponent space minus space 16 space equals space 0


t = 4

t = -4

t = 16

t = 256

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Solve the equation for b.

square root of b space plus thin space 1 end root space equals space square root of b space plus space 6 end root space minus space 1


b = 3

b = -2

b = -3

No solution

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Solve the equation for x.

left parenthesis 2 x space plus space 4 right parenthesis to the power of 1 fifth end exponent space plus space 2 space equals space 4


x = 211

x = -2

x = 18

x = 14

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When an object is dropped from the top of a 50-foot tall building, the object will be h feet above the ground after t seconds, where 1 half square root of 50 space minus space h end root space equals space t. How far above the ground will the object be after 1 second?


34 feet

46 feet

48 feet

3.5 feet

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