# Worksheet: 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 negative number.
• BIt is a natural number.
• CIt is an irrational number.
• DIt is a rational number.
• EIt is an integer number.

Q2:

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

• A15 inches by 15 inches
• B9 inches by 9 inches
• C13 inches by 13 inches
• D18 inches by 18 inches

Q3:

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

• A22 ft by 22 ft
• B23 ft by 23 ft
• C16 ft by 16 ft
• D18 ft by 18 ft
• E32 ft by 32 ft

Q4:

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

• A16 cm by 16 cm
• B17 cm by 17 cm
• C9 cm by 9 cm
• D14 cm by 14 cm
• E18 cm by 18 cm

Q5:

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

• A19 cm by 19 cm
• B26 cm by 26 cm
• C17 cm by 17 cm
• D20 cm by 20 cm
• E34 cm by 34 cm

Q6:

Determine the square of the number whose cube is .

Q7:

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

• A18.4 cm by 18.4 cm
• B57.6 cm by 57.6 cm
• C14.4 cm by 14.4 cm
• D16.4 cm by 16.4 cm
• E28.8 cm by 28.8 cm

Q8:

The side length, , of a cube is given by the formula , where is the volume of the cube. What is the side length of a cube whose volume is 5 832 cm3?

Q9:

Find the volume of the cube, given that the length of its edge is cm.

• A22 cm3
• B cm3
• C12 cm3
• D cm3

Q10:

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

• A84 cm
• B168 cm
• C cm
• D cm
• E cm

Q11:

A square has a side length of cm and an area of 63 cm2. Find the area of a square whose side length is cm.

• A378 cm2
• B cm2
• C
2 268
cm2
• D cm2
• E99 cm2

Q12:

Given that , , and , determine the length of .

Q13:

Given that the dimensions of a rectangle are cm and cm, find the length of its perimeter.

Q14:

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

Q15:

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

• A cm
• B cm
• C cm
• D cm

Q16:

Sophia bought enough lawn fertilizer to cover 256 square feet. What are the dimensions of the largest square plot of lawn this amount of fertilizer can cover?

• A26 ft by 26 ft
• B16 ft by 16 ft
• C18 ft by 18 ft
• D32 ft by 32 ft