Pythagorean Theorem by Simplifying Radicals

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.

• √181

• 90

• 19

• √19

Solve for x. SIMPLIFY your radical answer completely.

• 2√6

• 6√2

• 4√6

• 6√4

Solve for x. SIMPLIFY your radical answer completely.

• 4√2

• 2√4

• 2√2

• 16√2

What is the measure of a?

• 3

• 3√3

• 6

• 3√2

Find the most simplified radical AND approximate answers for x.

• √277 ≈ 16.6

• 115

• √115 ≈ 10.7

Find the most simplified radical AND approximate answers for x.

• 13√2 ≈ 18.4

• 2√13 ≈ 7.2

• 4√13 ≈ 14.4

Find the most simplified radical AND approximate answers for x.

• 21√2 ≈ 29.7

• 2√21 ≈ 9.2

• √116 ≈ 10.8

A 10-foot ladder is leaning against the wall.  The bottom of the ladder is 4 feet from the base of the wall.  Which of the following is closest to the distance from the top of the ladder to the base of the wall?

• 9ft

• 11ft

• 6ft

• 14ft

What is the formula used to solve for the hypotenuse?

• a² + b² = c²

• a + b = c

• a - b = c

• c - a = c