Worksheet: Square Roots of Perfect Squares

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In this worksheet, we will practice finding square roots of perfect square integers, fractions, and decimals.

Q1:

Calculate √1+√4+√9+√400+√841+√900+√961.

Q2:

Find the two square roots of 49.

  • A 2 3
  • B 3 2 , − 3 2
  • C 4 9 , − 4 9
  • D 2 3 , − 2 3
  • E − 2 3

Q3:

Replace 𝑥 by a positive number to make 169=𝑥 true.

  • A 2 3
  • B 4 9
  • C 8 3
  • D 4 3
  • E 1 6 3

Q4:

Calculate 19625.

  • A 1 4 5
  • B 1 8 5
  • C 9 8 1 2
  • D 1 4 9

Q5:

Calculate √81×16.

Q6:

Solve 𝑥=16169.

  • A 𝑥 = 1 or 𝑥=16169
  • B 𝑥 = 4 1 3 or 𝑥=−413
  • C 𝑥 = 1 6 9 1 6 or 𝑥=−16916
  • D 𝑥 = 1 3 4 or 𝑥=−134
  • E 𝑥 = 1 6 1 6 9 or 𝑥=−16169

Q7:

Evaluate √36.

  • A9 or −9
  • B18 or −18
  • C18
  • D6 or −6
  • E6

Q8:

Calculate the following: √4.

Q9:

Calculate −√0.25.

  • A − 1 2
  • B − 1
  • C − 5 3
  • D − 5 2

Q10:

Evaluate −√0.000169.

Q11:

Find −441529.

  • A − 1 2 3
  • B 2 3 2 1
  • C 2 1 2 3
  • D − 2 3 2 1
  • E − 2 1 2 3

Q12:

Calculate ±361100.

  • A 1 9 1 0 , − 1 9 1 0
  • B 1 9 2 9 , − 1 9 2 9
  • C 7 5 0 , − 7 5 0
  • D 7 1 0 , − 7 1 0

Q13:

A squared mosaic is made up of 1,800 white squares and 1,800 black squares of equal sizes. Determine the number of squares required to make one side of the mosaic.

Q14:

Find the value of √144.

  • A6
  • B18 or −18
  • C12
  • D6 or −6
  • E12 or −12

Q15:

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

Q16:

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

  • Aa rational number
  • Ban irrational number

Q17:

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?

Q18:

Given that (𝑋𝑌)=100cm and 𝑍 is the midpoint of 𝑋𝑌, determine the length of 𝑋𝑍.

  • A25 cm
  • B5 cm
  • C50 cm
  • D 5 2 cm

Q19:

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.

Q20:

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.

Q21:

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

Q22:

Evaluate √625.

Q23:

Evaluate 916.

  • A 3 4 or −34
  • B 3 1 6
  • C 9 4 or −94
  • D 3 1 6 or −316
  • E 3 4

Q24:

Determine the square roots of 1,156.

  • A37, −37
  • B68, −68
  • C43, −43
  • D34, −34

Q25:

Given that 𝑥𝑦=259, evaluate 𝑥𝑦.

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

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