Exam 7: Radical Expressions and Equations

Perform the indicated operation. Assume all variables represent positive numbers. $\left( 9 x ^ { - 12 } \right) ^ { - \frac { 1 } { 2 } }$

Multiply and simplify, if possible. $8 \sqrt { m n ^ { 3 } } ( 5 \sqrt { m n } )$

The __________ of $\sqrt { x } + 3$ is $\sqrt { x } - 3$ .

Rationalize the denominator. $\frac { \sqrt { 3 } + \sqrt { 2 } } { \sqrt { 3 } - \sqrt { 2 } }$

Simplify: $16 ^ { \frac { 3 } { 2 } }$

Find $f ( - 4 )$ , given $f ( x ) = \sqrt [ 3 ] { x - 23 }$

Solve: $\sqrt { x } + 2 = \sqrt { 2 x + 7 }$

Perform the operation. Write the answer in the form $a + b i$ . $( 6 + \sqrt { - 4 } ) + ( 8 + \sqrt { - 9 } )$

Perform the indicated operation. Simplify, if possible. $3 x \sqrt [ 4 ] { 96 x } - 4 \sqrt [ 4 ] { 486 x ^ { 5 } }$

Square both sides of the equation. $\sqrt { x + 3 } + 2 = \sqrt { x - 1 }$

Simplify the expression. Assume that x is unrestricted and use absolute value symbols if necessary. $\sqrt { 9 x ^ { 2 } }$

Perform the operation. Write the answer in the form $a + b i$ . $( 3 + 4 i ) + ( 5 - 9 i )$

In the expression $\sqrt [ 3 ] { 27 x ^ { 6 } }$ , the index is 3 and $27 x ^ { 6 }$ is the __________.

Multiply. $\sqrt { - 2 } \sqrt { - 14 }$

Simplify the expression. $i^{29}$

The lengths of two sides of the right triangle ABC are given. Find the length of the missing side. a=3 ft and b=4 ft c= __________ ft

Square the quantity and simplify the result, if possible. $( 2 \sqrt { 2 r } - 1 ) ^ { 2 }$

Multiply: $\sqrt [ 4 ] { 6 } \cdot \sqrt [ 8 ] { 6 }$

Find the missing lengths in the triangle. Give the answer to two decimal places. x= __________ y= __________

Multiply. Write the answer in the form $a + b i$ . $( 5 - 3 i ) ( 3 + 5 i )$