Class 8 Maths Worksheet: Squares and Square Roots

Maths worksheets lesson 58: Squares and square roots · Set 284 · 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 smallest whole number by which 1053 must be divided to get a perfect square?
2. 2.What is the sum of the first 18 odd numbers (1 + 3 + 5 + …)?
3. 3.What is the sum of the first 7 odd numbers (1 + 3 + 5 + …)?
4. 4.What is √2704? =
5. 5.How many whole numbers lie between 20² and 21²?
6. 6.Which of these is a perfect square? (a) 1123 (b) 1089 (c) 1098
7. 7.How many whole numbers lie between 35² and 36²?
8. 8.What is the smallest whole number by which 1134 must be divided to get a perfect square?
9. 9.A square garden has an area of 2025 square m. How long is each side (in m)?
10. 10.What is 87²? =
11. 11.What is √324? =
12. 12.What is the sum of the first 10 odd numbers (1 + 3 + 5 + …)?
13. 13.Which of these is a perfect square? (a) 256 (b) 284 (c) 272
14. 14.What is √2809? =
15. 15.What is 51²? =
16. 16.What is 86²? =
17. 17.What is the smallest whole number by which 135 must be multiplied to get a perfect square?
18. 18.What is √1849? =
19. 19.What is √484? =
20. 20.What is √9025? =
21. 21.What is the smallest whole number by which 325 must be multiplied to get a perfect square?
22. 22.What is the smallest whole number by which 240 must be divided to get a perfect square?
23. 23.How many whole numbers lie between 19² and 20²?
24. 24.Which of these is a perfect square? (a) 250 (b) 225 (c) 231
25. 25.Which of these is a perfect square? (a) 327 (b) 324 (c) 329
26. 26.What is the smallest whole number by which 320 must be multiplied to get a perfect square?
27. 27.What is 42²? =
28. 28.What is 20²? =
29. 29.What is 24²? =
30. 30.How many whole numbers lie between 34² and 35²?
31. 31.How many whole numbers lie between 36² and 37²?
32. 32.What is the smallest whole number by which 384 must be divided to get a perfect square?
33. 33.What is the smallest whole number by which 99 must be multiplied to get a perfect square?
34. 34.What is the smallest whole number by which 375 must be divided to get a perfect square?
35. 35.What is √1089? =
36. 36.What is 97²? =
37. 37.What is the sum of the first 24 odd numbers (1 + 3 + 5 + …)?
38. 38.What is √6241? =
39. 39.What is the smallest whole number by which 28 must be divided to get a perfect square?
40. 40.What is the smallest whole number by which 48 must be divided to get a perfect square?

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