Class 8 Maths Worksheet: Squares and Square Roots

Maths worksheets lesson 58: Squares and square roots · Set 273 · 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.What is 83²? =
2. 2.Which of these is a perfect square? (a) 263 (b) 280 (c) 256
3. 3.Which of these is a perfect square? (a) 818 (b) 805 (c) 784
4. 4.Which of these is a perfect square? (a) 625 (b) 655 (c) 661
5. 5.What is √1849? =
6. 6.A square garden has an area of 1296 square m. How long is each side (in m)?
7. 7.Which of these is a perfect square? (a) 443 (b) 441 (c) 483
8. 8.What is 71²? =
9. 9.Which of these is a perfect square? (a) 196 (b) 217 (c) 220
10. 10.What is √625? =
11. 11.What is √1521? =
12. 12.What is the sum of the first 21 odd numbers (1 + 3 + 5 + …)?
13. 13.What is 89²? =
14. 14.What is the smallest whole number by which 90 must be divided to get a perfect square?
15. 15.A square garden has an area of 1089 square m. How long is each side (in m)?
16. 16.What is 52²? =
17. 17.What is 99²? =
18. 18.What is √8649? =
19. 19.What is 62²? =
20. 20.What is the smallest whole number by which 63 must be divided to get a perfect square?
21. 21.What is the sum of the first 7 odd numbers (1 + 3 + 5 + …)?
22. 22.A square garden has an area of 1225 square m. How long is each side (in m)?
23. 23.A square garden has an area of 900 square m. How long is each side (in m)?
24. 24.What is 69²? =
25. 25.What is the smallest whole number by which 176 must be multiplied to get a perfect square?
26. 26.A square garden has an area of 441 square m. How long is each side (in m)?
27. 27.What is the sum of the first 22 odd numbers (1 + 3 + 5 + …)?
28. 28.What is the smallest whole number by which 252 must be divided to get a perfect square?
29. 29.What is the smallest whole number by which 150 must be multiplied to get a perfect square?
30. 30.How many whole numbers lie between 21² and 22²?
31. 31.What is the smallest whole number by which 375 must be multiplied to get a perfect square?
32. 32.How many whole numbers lie between 16² and 17²?
33. 33.What is √8464? =
34. 34.What is the sum of the first 17 odd numbers (1 + 3 + 5 + …)?
35. 35.What is 12²? =
36. 36.What is 25²? =
37. 37.How many whole numbers lie between 12² and 13²?
38. 38.What is 16²? =
39. 39.What is the smallest whole number by which 1215 must be multiplied to get a perfect square?
40. 40.How many whole numbers lie between 8² and 9²?

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