Class 8 Maths Worksheet: Squares and Square Roots

Maths worksheets lesson 58: Squares and square roots · Set 262 · 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.How many whole numbers lie between 20² and 21²?
2. 2.What is 60²? =
3. 3.What is the smallest whole number by which 176 must be multiplied to get a perfect square?
4. 4.What is √5776? =
5. 5.What is the sum of the first 6 odd numbers (1 + 3 + 5 + …)?
6. 6.What is √1225? =
7. 7.What is √6561? =
8. 8.What is the sum of the first 18 odd numbers (1 + 3 + 5 + …)?
9. 9.What is 96²? =
10. 10.What is √400? =
11. 11.Which of these is a perfect square? (a) 1371 (b) 1404 (c) 1369
12. 12.Which of these is a perfect square? (a) 256 (b) 283 (c) 264
13. 13.A square garden has an area of 529 square m. How long is each side (in m)?
14. 14.What is the sum of the first 29 odd numbers (1 + 3 + 5 + …)?
15. 15.What is the smallest whole number by which 896 must be divided to get a perfect square?
16. 16.What is the smallest whole number by which 40 must be divided to get a perfect square?
17. 17.Which of these is a perfect square? (a) 1506 (b) 1445 (c) 1444
18. 18.What is 24²? =
19. 19.What is the smallest whole number by which 135 must be multiplied to get a perfect square?
20. 20.A square garden has an area of 1156 square m. How long is each side (in m)?
21. 21.What is 30²? =
22. 22.What is √8100? =
23. 23.What is the sum of the first 21 odd numbers (1 + 3 + 5 + …)?
24. 24.A square garden has an area of 576 square m. How long is each side (in m)?
25. 25.What is √1849? =
26. 26.A square garden has an area of 169 square m. How long is each side (in m)?
27. 27.A square garden has an area of 1936 square m. How long is each side (in m)?
28. 28.What is the sum of the first 13 odd numbers (1 + 3 + 5 + …)?
29. 29.What is the smallest whole number by which 243 must be divided to get a perfect square?
30. 30.A square garden has an area of 256 square m. How long is each side (in m)?
31. 31.What is 81²? =
32. 32.How many whole numbers lie between 22² and 23²?
33. 33.What is 54²? =
34. 34.What is the sum of the first 27 odd numbers (1 + 3 + 5 + …)?
35. 35.How many whole numbers lie between 12² and 13²?
36. 36.Which of these is a perfect square? (a) 1026 (b) 1024 (c) 1080
37. 37.What is 39²? =
38. 38.What is the sum of the first 11 odd numbers (1 + 3 + 5 + …)?
39. 39.How many whole numbers lie between 14² and 15²?
40. 40.A square garden has an area of 2025 square m. How long is each side (in m)?

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