Pythagorean Theorem and Simplifying Radicals

Simplify into simplest radical form: $$\sqrt[]{512}$$

Simplify $$\sqrt[]{75}$$ into simplest radical form.

Find the value of y. Express in simplest radical form.

Find the value of y. Express in simplest radical form.

Find the value of y. Express in simplest radical form.

Find the value of y. Express in simplest radical form.

Find the value of y. Express in simplest radical form. Options: $$\sqrt[]{30}$$ , 30, $$\sqrt[]{900}$$ , 900

A square has a side length of 10 yds. What is the length of the diagonal of the square?

A repairman leans the top of an 8-ft ladder against the top of a stone wall. The base of the ladder is 6 ft from the wall. How tall is the wall?

A river runs straight through the center of a park. A man stands on one bank of the river, and his daughter stands across the river and 22 ft upstream. The man's son swims from the man to his daughter. If the river is 11 ft wide, how far does the son swim?