Pythagorean Theorem and Radical Fun

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? Express in simplest radical form.

• 10

A square has a side length of 10 yds. What is the length of the diagonal of the square? Express in simplest radical form.

• 200

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? Express in simplest radical form.

Solve for x. SIMPLIFY your radical answer completely.

• 4√2

• 2√4

• 2√2

• 16√2

Solve for x. SIMPLIFY your radical answer completely.

• 119

• √119

• 13

• √13

Solve for x. SIMPLIFY your radical answer completely.

• 2√6

• 6√2

• 4√6

• 6√4

Solve for x. SIMPLIFY your radical answer completely.

• √3

• 3

• √41

• 41

Solve for x. SIMPLIFY your radical answer completely.

• √181

• 90

• 19

• √19

Find the most simplified radical AND approximate answers for x.

• 21√2 ≈ 29.7

• 2√21 ≈ 9.2

• √116 ≈ 10.8

Find the most simplified radical AND approximate answers for x.

• 13√2 ≈ 18.4

• 2√13 ≈ 7.2

• 4√13 ≈ 14.4