Radical Expressions & Equations: 8th Grade Challenge

A square garden has an area of 144 square feet. What is the length of one side of the garden? Simplify your answer using a radical expression.

• 16

• 12

• 14

• 10

A right triangle has one leg measuring 6 feet and the other leg measuring 8 feet. What is the length of the hypotenuse? Use a radical expression to express your answer.

• 12 feet

• 8 feet

• 10 feet

• 14 feet

The length of a rectangular swimming pool is 10 feet longer than its width. If the area of the pool is 300 square feet, find the width using a radical equation.

• 5(√13 - 1)

• 8(√5 - 3)

• 4(√15 - 2)

• 6(√10 - 1)

A ladder is leaning against a wall, forming a right triangle with the ground. If the base of the ladder is 4 feet from the wall and the ladder is 8 feet long, how high up the wall does the ladder reach? Solve using a radical equation.

• 5 feet

• 4√3 feet

• 6 feet

• 3√2 feet

A square has a perimeter of 40 meters. What is the length of one side expressed as a simplified radical?

• √(80)

• √(64)

• √(36)

• √(100)

The area of a circular garden is 50π square meters. What is the radius of the garden? Provide your answer in simplified radical form.

• 5√3

• 4√2

• 10

• 5√2

A rectangular box has a volume of 64 cubic inches. If the height is 4 inches, what is the area of the base? Use a radical expression to find your answer.

• 20

• 12

• 24

• 16

A triangle has a base of 12 cm and an area of 36 cm². What is the height of the triangle? Solve using a radical equation.

• 4 cm

• 8 cm

• 6 cm

• 10 cm

The diagonal of a square is 10√2 cm. What is the length of one side of the square? Simplify your answer using a radical expression.

• 5√2 cm

• 15 cm

• 20 cm

• 10

A cone has a radius of 3 cm and a height of 4 cm. What is the slant height of the cone? Use a radical expression to express your answer.

• 5 cm

• 7 cm

• 6 cm

• 4 cm