Exam 7: Radical Expressions and Equations

Simplify the expression. Write the answer without negative exponents. $\frac { 6 ^ { \frac { 5 } { 6 } } 6 ^ { \frac { 1 } { 3 } } } { 6 ^ { \frac { 1 } { 2 } } }$

Evaluate the expression. $125 ^ { \frac { 2 } { 3 } }$

One side of a square is 9 inches long. Find the length of its diagonal. Give the exact answer.

The largest perfect-square _________ of 50 is 25.

Evaluate the expression. $625 ^ { \frac { 1 } { 4 } }$

Find the height h of the ironing board shown in the illustration. Find the exact answer. Then give an approximation to two decimal places.

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

An __________ right triangle is a right triangle with two legs of equal length.

Perform the indicated operation. Simplify, if possible. $\sqrt [ 3 ] { 54 x ^ { 4 } } - x ^ { 3 } \sqrt { - 16 x }$

Find the distance between the points (0,-5)and (3,5).

Proposed solutions of a radical equation that don't satisfy it are called _________ solutions.

Square the quantity and simplify the result, if possible. $( 2 \sqrt { 11 } ) ^ { 2 }$

The complex conjugate of $3 - 4 i$ is _________.

Simplify $\sqrt { ( - 10 b ) ^ { 2 } }$ . Assume all variables are unrestricted.

Write $1 + \sqrt { - 63 }$ in the form a+bi

Simplify: $\sqrt { 32 }$

Simplify: $\sqrt [ 3 ] { - 54 x ^ { 11 } y ^ { 9 } }$

Simplify the expression. Assume that x is unrestricted and use absolute value symbols if necessary. $\sqrt { 36 x ^ { 2 } }$

Simplify $8 \sqrt { 49 x + 49 } - 4 \sqrt { x + 1 }$ . All variables represent positive real numbers.

Find the exact length of the diagonal of a cube that has sides of 8 inches in length.