Class 8 Maths Worksheet: Squares and Square Roots

Maths worksheets lesson 58: Squares and square roots · Set 290 · 40 sums

The method (Pairs make squares): Square: n × n. Quick way: (a + b)² = a² + 2ab + b², e.g. 42² = 1600 + 160 + 4. Square root: the number that times itself gives the square; a square ending in 4 has a root ending in 2 or 8. Make a perfect square: break into primes; multiply (or divide) by the prime left without a partner. 1 + 3 + 5 + … (n odd numbers) = n². Between n² and (n + 1)² there are 2n whole numbers.

1. 1.Which of these is a perfect square? (a) 453 (b) 441 (c) 452
2. 2.Which of these is a perfect square? (a) 650 (b) 625 (c) 665
3. 3.What is the smallest whole number by which 44 must be divided to get a perfect square?
4. 4.What is 19²? =
5. 5.Which of these is a perfect square? (a) 269 (b) 272 (c) 256
6. 6.What is 69²? =
7. 7.What is √324? =
8. 8.A square garden has an area of 484 square m. How long is each side (in m)?
9. 9.How many whole numbers lie between 11² and 12²?
10. 10.Which of these is a perfect square? (a) 1095 (b) 1104 (c) 1089
11. 11.What is 41²? =
12. 12.What is the sum of the first 12 odd numbers (1 + 3 + 5 + …)?
13. 13.Which of these is a perfect square? (a) 144 (b) 155 (c) 165
14. 14.What is 75²? =
15. 15.A square garden has an area of 1521 square m. How long is each side (in m)?
16. 16.What is √729? =
17. 17.What is 96²? =
18. 18.What is 91²? =
19. 19.What is the sum of the first 14 odd numbers (1 + 3 + 5 + …)?
20. 20.What is √3249? =
21. 21.Which of these is a perfect square? (a) 1296 (b) 1307 (c) 1302
22. 22.What is the sum of the first 8 odd numbers (1 + 3 + 5 + …)?
23. 23.Which of these is a perfect square? (a) 902 (b) 910 (c) 900
24. 24.A square garden has an area of 2116 square m. How long is each side (in m)?
25. 25.What is √1296? =
26. 26.What is √5776? =
27. 27.What is √441? =
28. 28.Which of these is a perfect square? (a) 576 (b) 620 (c) 612
29. 29.What is 27²? =
30. 30.How many whole numbers lie between 46² and 47²?
31. 31.How many whole numbers lie between 39² and 40²?
32. 32.What is √484? =
33. 33.How many whole numbers lie between 15² and 16²?
34. 34.What is the sum of the first 21 odd numbers (1 + 3 + 5 + …)?
35. 35.What is √4356? =
36. 36.What is the smallest whole number by which 48 must be multiplied to get a perfect square?
37. 37.What is the sum of the first 11 odd numbers (1 + 3 + 5 + …)?
38. 38.What is √1764? =
39. 39.What is 80²? =
40. 40.What is 59²? =

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