# Worksheet: Square Roots of Perfect Squares

Q1:

Calculate the side length of a square whose area is 6β400 dm2.

Q2:

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

• A a rational number
• B an irrational number

Q3:

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 canβ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?

Q4:

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

• A cm
• B 50 cm
• C 25 cm
• D 5 cm

Q5:

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.

Q6:

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.

Q7:

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.

Q8:

Mr. Michaelβ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 312β423 ft2
• B 216β350 ft2
• C 408β367 ft2
• D 190β096 ft2
• E 209β740 ft2

Q9:

Evaluate .

Q10:

Evaluate .

• A or
• B or
• C
• D
• E or

Q11:

Determine the square roots of 1β156.

• A43,
• B68,
• C37,
• D34,

Q12:

Given that , evaluate .

• A
• B
• C
• D

Q13:

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

Q14:

The area of a park is 197β136 square feet. If the borders of the park are of the same length, determine the length of each side.

Q15:

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 1β764 ft2
• E 868 ft2