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Worksheet: Solving Real-World Problems including Radical Expressions

Q1:

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

  • 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:

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

Q3:

Emma’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

Q4:

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

Q5:

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

Q6:

Determine the square of the number whose cube is βˆ’ 5 1 2 .

Q7:

Noah 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

Q8:

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

  • A √ 2 1 cm
  • B 2 √ 4 2 cm
  • C 168 cm
  • D 8 √ 2 1 cm
  • E 84 cm

Q9:

Given that ( 𝐴 𝐡 ) = 4 2 2 c m , ( 𝐡 𝐢 ) = 1 6 2 2 c m , and 𝐡 ∈ 𝐴 𝐢 , determine the length of 𝐴 𝐢 .

Q10:

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

Q11:

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

  • A 2 4 √ 6 cm
  • B 2 8 √ 6 cm
  • C 3 2 √ 6 cm
  • D 1 2 √ 6 cm