Class 8 Maths Worksheet: Squares and Square Roots

Maths worksheets lesson 58: Squares and square roots · Set 77 · 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) 125 (b) 121 (c) 132
2. 2.What is √5929? =
3. 3.Which of these is a perfect square? (a) 1625 (b) 1600 (c) 1649
4. 4.What is √3969? =
5. 5.How many whole numbers lie between 34² and 35²?
6. 6.What is √4489? =
7. 7.Which of these is a perfect square? (a) 281 (b) 274 (c) 256
8. 8.What is √8836? =
9. 9.What is the smallest whole number by which 396 must be divided to get a perfect square?
10. 10.Which of these is a perfect square? (a) 486 (b) 521 (c) 484
11. 11.What is √1600? =
12. 12.What is the sum of the first 17 odd numbers (1 + 3 + 5 + …)?
13. 13.What is the smallest whole number by which 208 must be multiplied to get a perfect square?
14. 14.What is the smallest whole number by which 18 must be multiplied to get a perfect square?
15. 15.What is 77²? =
16. 16.What is the sum of the first 24 odd numbers (1 + 3 + 5 + …)?
17. 17.Which of these is a perfect square? (a) 529 (b) 549 (c) 553
18. 18.Which of these is a perfect square? (a) 625 (b) 632 (c) 634
19. 19.What is √1296? =
20. 20.A square garden has an area of 225 square m. How long is each side (in m)?
21. 21.What is 39²? =
22. 22.What is √3844? =
23. 23.What is the smallest whole number by which 704 must be multiplied to get a perfect square?
24. 24.How many whole numbers lie between 35² and 36²?
25. 25.What is 15²? =
26. 26.What is the smallest whole number by which 891 must be multiplied to get a perfect square?
27. 27.Which of these is a perfect square? (a) 203 (b) 221 (c) 196
28. 28.A square garden has an area of 36 square m. How long is each side (in m)?
29. 29.Which of these is a perfect square? (a) 1180 (b) 1156 (c) 1160
30. 30.How many whole numbers lie between 17² and 18²?
31. 31.What is √729? =
32. 32.How many whole numbers lie between 44² and 45²?
33. 33.What is √1681? =
34. 34.What is 33²? =
35. 35.How many whole numbers lie between 23² and 24²?
36. 36.What is the sum of the first 25 odd numbers (1 + 3 + 5 + …)?
37. 37.What is √256? =
38. 38.What is the smallest whole number by which 243 must be multiplied to get a perfect square?
39. 39.What is 93²? =
40. 40.Which of these is a perfect square? (a) 743 (b) 781 (c) 729

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