Exam 7: Radical Expressions and Equations

Perform the indicated operation. Simplify, if possible. Assume all variables are positive. $\sqrt { 12 x ^ { 9 } y ^ { 9 } } \cdot \sqrt { 8 x ^ { 2 } y ^ { 4 } }$

Perform the operation. Write the answer in the form $a + b i$ . $( - 6 + \sqrt { - 81 } ) - ( - 3 - \sqrt { - 64 } )$

If a and b are the lengths of the legs of a right triangle and c is the length of the hypotenuse, then __________.

Equations such as $\sqrt { x + 4 } - 7 = 5$ and $\sqrt [ 3 ] { x + 1 } = 13$ are called __________ equations.

Multiply: $\sqrt { 3 } \cdot \sqrt [ 4 ] { 3 }$

Simplify by combining like radicals. $4 \sqrt [ 3 ] { 32 } - \sqrt [ 3 ] { 256 } - 5 \sqrt [ 3 ] { 108 }$

Simplify by combining like radicals. $\sqrt { 75 } - \sqrt { 48 } - \sqrt { 147 }$

Evaluate the square root, if possible, without using a calculator. $\sqrt { 100 }$

Perform the indicated operation. $\frac { 7 - 5 i } { 3 + 2 i }$

Simplify the radical expression. The variable represents a positive real number. $\sqrt [ 3 ] { - 48 x ^ { 6 } }$

Evaluate the square root, if possible, without using a calculator. $\sqrt { \frac { 1 } { 81 } }$

Radical expressions such as $\sqrt [ 3 ] { 5 }$ and $2 \sqrt [ 3 ] { 5 }$ with the same index and the same radicand are called __________ radicals.

In a right triangle, the side opposite the 90 ^∘ angle is called the __________.

Find the exact length of the diagonal (in blue) of one of one of the faces of the cube.

Simplify: $i^{10}$

Simplify the expression. The variable represents a positive real number. $- \left( 16 x ^ { 6 } \right) ^ { - \frac { 3 } { 2 } }$

Find the domain of $f ( x ) = \sqrt { 8 - x }$ .

Find the value given that $g ( x ) = \sqrt [ 3 ] { x - 4 }$ . $g ( 5 ) = ?$

Simplify the expression. $36 ^ { - \frac { 1 } { 2 } }$

Simplify the expression. $\sqrt [ 4 ] { 64 }$