Class 8 Maths Worksheet: Squares and Square Roots

Maths worksheets lesson 58: Squares and square roots · Set 4 · 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 the sum of the first 12 odd numbers (1 + 3 + 5 + …)?
2. 2.How many whole numbers lie between 34² and 35²?
3. 3.Which of these is a perfect square? (a) 704 (b) 707 (c) 676
4. 4.What is the smallest whole number by which 1215 must be divided to get a perfect square?
5. 5.What is the sum of the first 19 odd numbers (1 + 3 + 5 + …)?
6. 6.What is 87²? =
7. 7.What is the smallest whole number by which 448 must be divided to get a perfect square?
8. 8.What is the smallest whole number by which 99 must be multiplied to get a perfect square?
9. 9.How many whole numbers lie between 37² and 38²?
10. 10.Which of these is a perfect square? (a) 1645 (b) 1643 (c) 1600
11. 11.What is √1156? =
12. 12.What is √9216? =
13. 13.What is 62²? =
14. 14.Which of these is a perfect square? (a) 1156 (b) 1167 (c) 1189
15. 15.What is the smallest whole number by which 686 must be multiplied to get a perfect square?
16. 16.What is √144? =
17. 17.What is the sum of the first 11 odd numbers (1 + 3 + 5 + …)?
18. 18.What is the smallest whole number by which 208 must be divided to get a perfect square?
19. 19.Which of these is a perfect square? (a) 214 (b) 208 (c) 196
20. 20.What is √729? =
21. 21.Which of these is a perfect square? (a) 525 (b) 484 (c) 488
22. 22.How many whole numbers lie between 15² and 16²?
23. 23.What is the smallest whole number by which 360 must be multiplied to get a perfect square?
24. 24.Which of these is a perfect square? (a) 798 (b) 801 (c) 784
25. 25.What is 45²? =
26. 26.What is 56²? =
27. 27.How many whole numbers lie between 43² and 44²?
28. 28.What is the smallest whole number by which 98 must be divided to get a perfect square?
29. 29.What is √6241? =
30. 30.What is the smallest whole number by which 50 must be multiplied to get a perfect square?
31. 31.Which of these is a perfect square? (a) 138 (b) 128 (c) 121
32. 32.What is 73²? =
33. 33.How many whole numbers lie between 27² and 28²?
34. 34.What is 65²? =
35. 35.Which of these is a perfect square? (a) 320 (b) 289 (c) 299
36. 36.What is the smallest whole number by which 1134 must be divided to get a perfect square?
37. 37.What is the sum of the first 13 odd numbers (1 + 3 + 5 + …)?
38. 38.How many whole numbers lie between 46² and 47²?
39. 39.What is the sum of the first 24 odd numbers (1 + 3 + 5 + …)?
40. 40.What is the sum of the first 7 odd numbers (1 + 3 + 5 + …)?

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