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Worksheet: Solving Real-World Problems Including Radical Expressions


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.


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


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


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


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


Determine the square of the number whose cube is .


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


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?


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

  • A22 cm3
  • B cm3
  • C12 cm3
  • D cm3


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


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
  • D cm2
  • E99 cm2


Given that , , and , determine the length of .


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


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


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

  • A cm
  • B cm
  • C cm
  • D cm


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

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