# Worksheet: Applications of Radical Expressions

In this worksheet, we will practice solving real-world problems including radical expressions.

Q1:

A square of side length cm has an area of 280 cm2. Which of the following is true about ?

• AIt is a rational number.
• BIt is an integer number.
• CIt is a natural number.
• DIt is an irrational number.
• EIt is a negative number.

Q2:

Determine the dimensions of a square-shaped chessboard having an area of 81 square centimeters.

• A 14 cm by 14 cm
• B 18 cm by 18 cm
• C 17 cm by 17 cm
• D 9 cm by 9 cm
• E 16 cm by 16 cm

Q3:

Given that the area of each square on the chessboard is 21 cm2, find the length of the chessboardβs side.

• A cm
• B cm
• C 168 cm
• D cm
• E 84 cm

Q4:

Determine the area of the isosceles triangle , given that , , cm, and cm.

Q5:

Adel bought a squared greeting card of area 207.36 square centimeters. Find the dimensions of the greeting card.

• A 16.4 cm by 16.4 cm
• B 28.8 cm by 28.8 cm
• C 57.6 cm by 57.6 cm
• D 14.4 cm by 14.4 cm
• E 18.4 cm by 18.4 cm

Q6:

Given that , , and , determine the length of .

Q7:

Given that a square tile has an area of 81 square inches, determine the dimensions of the tile.

• A 13 inches by 13 inches
• B 18 inches by 18 inches
• C 15 inches by 15 inches
• D 9 inches by 9 inches

Q8:

Sarahβs bedroom is shaped like a square. Determine the dimensions of her room if the area of its floor is 256 ft2.

• A 18 ft by 18 ft
• B 32 ft by 32 ft
• C 23 ft by 23 ft
• D 16 ft by 16 ft
• E 22 ft by 22 ft

Q9:

Determine the square of the number whose cube is .

Q10:

What is the perimeter of the triangle ? Express your answer in its simplest form.

• A cm
• B cm
• C cm
• D cm

Q11:

Determine the dimensions of a square-shaped chessboard having an area of 289 square centimeters.

• A 20 cm by 20 cm
• B 34 cm by 34 cm
• C 26 cm by 26 cm
• D 17 cm by 17 cm
• E 19 cm by 19 cm