Operations with Radicals

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Operations with Radicals

Write the radical expression in simplest radical form.

square root of 200

A.

100

B.

10 square root of 2

C.

50 square root of 2

D.

25 square root of 2

Write the radical expression in simplest radical form.

cube root of 16 y to the power of 6 end root

A.

8 y space 3 root of 2 y cubed end root

B.

2 y space 3 root of 2 y cubed end root

C.

2 y squared space cube root of 2

D.

2 y space square root of 2

Write the radical expression in simplest radical form.

2 space 3 root of 32 m to the power of 5 n to the power of 7 end root

A. 4 m n squared space 3 root of 4 m squared n end root
B. 8 m n squared space 3 root of 2 m squared n end root
C. 2 m cubed n to the power of 6 space 3 root of 4 m squared n end root
D. 4 m cubed n to the power of 6 space 3 root of 4 m squared n end root

Write the radical expression in simplest form.

3 root of 3 over 4 end root

A.

3 root of 3 over 4 end root

B.

fraction numerator 3 root of 12 over denominator 4 end fraction

C.

fraction numerator 3 root of 6 over denominator 2 end fraction

D.

fraction numerator 3 root of 48 over denominator 4 end fraction

Write the radical expression in simplest radical form.

square root of fraction numerator 4 r to the power of 8 over denominator t to the power of 9 end fraction end root

A.

fraction numerator 2 r to the power of 4 over denominator t to the power of 4 space square root of t end fraction

B.

fraction numerator 2 r to the power of 4 space square root of t over denominator t to the power of 5 end fraction

C.

fraction numerator 2 r to the power of 4 t to the power of 4 space square root of t over denominator t to the power of 9 end fraction

D.

fraction numerator 2 r squared space square root of t to the power of 9 end root over denominator t to the power of 9 end fraction

Multiply the radical expressions and write in simplest radical form.

left parenthesis 2 square root of 32 right parenthesis left parenthesis minus 3 square root of 20 right parenthesis

A.

minus 48 square root of 10

B.

minus 384 square root of 10

C.

minus 6 square root of 640

D.

minus 480

Simplify the expression.

square root of 12 space plus thin space square root of 75 space minus space square root of 27

A.

20 square root of 3

B.

4 square root of 3

C.

square root of 60

D.

2 square root of 15

Simplify the expression and write in simplest radical form.

left parenthesis square root of 11 space minus space square root of 2 right parenthesis squared

A. 9
B. 9 space minus space square root of 22
C. 13 space minus space square root of 22
D. 13 space minus space 2 square root of 22

Simplify the expression and write in simplest radical form.

left parenthesis 3 thin space plus space square root of 7 right parenthesis left parenthesis 2 space plus thin space square root of 6 right parenthesis

A. 6 space plus space 10 square root of 6 space plus space 8 square root of 7
B. 6 space plus space 18 square root of 13
C. 36 space plus space 2 square root of 13
D. 6 space plus space 3 square root of 6 space plus thin space 2 square root of 7 space plus space square root of 42

Rationalize the denominator and write in simplest radical form.

fraction numerator square root of 6 over denominator 5 space plus space square root of 3 end fraction

A. fraction numerator 5 square root of 6 space minus space square root of 18 over denominator 22 end fraction
B. fraction numerator 5 square root of 6 space minus space 3 square root of 2 over denominator 22 end fraction
C. fraction numerator 5 square root of 6 space plus space square root of 18 over denominator 25 end fraction
D. fraction numerator 5 square root of 6 space plus space 3 square root of 2 over denominator 25 end fraction