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,
- B68,
- C37,
- D34,

**Q4: **

Evaluate .

**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 .

- A
- B
- C
- D
- E

**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 ft
^{2} - B
247 ft
^{2} - C
489 ft
^{2} - D
1 764 ft
^{2} - E
868 ft
^{2}

**Q9: **

Given that , evaluate .

- A
- B
- C
- D

**Q10: **

Given that and is the midpoint of , determine the length of .

- A 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 ft
^{2} - B
216,350 ft
^{2} - C
408,367 ft
^{2} - D
190,096 ft
^{2} - E
209,740 ft
^{2}

**Q12: **

Evaluate .

- A or
- B or
- C
- D
- E or

**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.