Exam 7: Roots, Radicals, and Complex Numbers

Write the word or phrase that best completes each statement or answers the question. - $\frac { \sqrt [ 5 ] { \mathrm { x } ^ { 14 } \mathrm { y } ^ { 16 } } } { \sqrt [ 3 ] { ( \mathrm { xy } ) ^ { 2 } } }$

Find the perimeter of the figure in radical form with the radicals simplified. -

Multiply. Write the result in the form a + bi. - $( 3 + 8 i ) ( 8 + 7 i )$

Divide. - $\frac { 3 i } { 2 + 3 i }$

Use absolute value to evaluate. - $\sqrt { ( - 2 ) ^ { 2 } }$

Divide. - $\frac { 2 } { 7 + i }$

Use absolute value to evaluate. - $\sqrt { ( 4 ) ^ { 2 } }$

Write the word or phrase that best completes each statement or answers the question. - $\frac { \sqrt [ 3 ] { x ^ { 11 } y ^ { 7 } } } { \sqrt { x y } }$

Simplify. - $\sqrt { 10 m ^ { 11 } { n }^{ 11} } \sqrt { 2 m n^ { 6 } }$

Simplify. - $\frac { \sqrt { 2 } } { \sqrt { 50 } }$

Simplify. Assume all variables represent positive real numbers. - $\sqrt { \frac { 108 x ^ { 7 } } { 4 y ^ { 7 } } }$

Solve and check your solution(s). If the equation has no real solution, so state. - $\sqrt { x ^ { 2 } } = \sqrt { x + 30 }$

Simplify. Assume all variables represent positive real numbers. - $\frac { 3 } { \sqrt { \mathrm { p } } }$

Simplify. - $\sqrt { y ^ { 9 } }$

Simplify the radical expression. Write the answer in radical form when appropriate. - $\left( \sqrt [ 4 ] { x ^ { 3 } y z ^ { 5 } } \right) ^ { 40 }$

Evaluate the radical expression if it is a real number. Use a calculator to approximate irrational numbers to the nearest hundredth. If the expression is not a real number, so state. - $\sqrt [ 3 ] { 343 }$

Write the word or phrase that best completes each statement or answers the question. - $\frac { \sqrt { ( x + y ) ^ { 10 } } } { \sqrt [ 4 ] { x + y } }$

Multiply. Write the result in the form a + bi. -( $( 8 + 7 i ) ( 7 - 6 i )$

Simplify. - $\sqrt { \frac { 1 } { 25 } }$

Evaluate if possible. If the expression is not a real number, so state. - $- 144 ^ { 1 / 2 }$