Worksheet: Square Roots of Perfect Squares Involving Integers

In this worksheet, we will practice finding the square root of a perfect square.

Q1:

Determine whether the square root of a perfect square is a rational or an irrational number.

  • A a rational number
  • B an irrational number

Q2:

Determine the square roots of 1‎ ‎156.

  • A43, 4 3
  • B68, 6 8
  • C37, 3 7
  • D34, 3 4

Q3:

Calculate the side length of a square whose area is 6,400 dm2.

Q4:

Evaluate 6 2 5 .

Q5:

The area of a park is 335‎ ‎241 square feet. If the borders of the park are of the same length, determine the length of each side.

Q6:

Simplify 1 6 4 𝑗 𝑘 𝑚 .

  • A 1 8 𝑗 𝑘 𝑚
  • B 1 6 4 | | 𝑗 𝑘 𝑚 | |
  • C 1 8 𝑗 𝑘 𝑚
  • D 1 8 | | 𝑗 𝑘 𝑚 | |
  • E 1 6 4 𝑗 𝑘 𝑚

Q7:

In a gymnasium, athletes perform their exercises on a square-shaped tumbling mat with an area of 1,681 square feet. Determine the distance an athlete has to run along one side of the mat.

Q8:

Which of the following can be the area of a square if the measure of its side length is a whole number?

  • A 531 ft2
  • B 247 ft2
  • C 489 ft2
  • D 1‎ ‎764 ft2
  • E 868 ft2

Q9:

Given that 𝑥 𝑦 = 2 5 9 , evaluate 𝑥 𝑦 .

  • A 1 2 5 3 , 1 2 5 3
  • B 5 3 , 5 3
  • C 1 2 5 9
  • D 1 2 5 2 7 , 1 2 5 2 7

Q10:

Given that ( 𝑋 𝑌 ) = 1 0 0 c m and 𝑍 is the midpoint of 𝑋 𝑌 , determine the length of 𝑋 𝑍 .

  • A 5 2 cm
  • B 50 cm
  • C 25 cm
  • D 5 cm

Q11:

Mr. Michael’s farm has a square-shaped field. Which of the following is the area of his field if its side lengths are measured in whole numbers?

  • A 312,423 ft2
  • B 216,350 ft2
  • C 408,367 ft2
  • D 190,096 ft2
  • E 209,740 ft2

Q12:

Evaluate 9 1 6 .

  • A 3 1 6 or 3 1 6
  • B 3 4 or 3 4
  • C 3 1 6
  • D 3 4
  • E 9 4 or 9 4

Q13:

An artist plans to make a large square mosaic out of 800 white and 800 black small square tiles. Unfortunately, 40 of the tiles are damaged, and can’t be used as part of the mosaic. The artist decides to make his mosaic as big a square as possible without using the damaged tiles. How many tiles will he end up not using in total?

Q14:

A chessboard has an area of 144 square inches, and there is a 1-inch border around the 64 squares on the board. Determine the length of one side of the region containing the small squares.

Q15:

In a gymnasium, athletes perform their exercises on a square-shaped tumbling mat with an area of 400 square feet. Determine the distance an athlete has to run along one side of the mat.

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