Class 8 Maths Worksheet: Squares and Square Roots

Maths worksheets lesson 58: Squares and square roots · Set 545 · 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 20²? =
2. 2.Which of these is a perfect square? (a) 1156 (b) 1201 (c) 1210
3. 3.What is the smallest whole number by which 48 must be multiplied to get a perfect square?
4. 4.What is the sum of the first 30 odd numbers (1 + 3 + 5 + …)?
5. 5.What is 52²? =
6. 6.What is the smallest whole number by which 637 must be multiplied to get a perfect square?
7. 7.What is the sum of the first 7 odd numbers (1 + 3 + 5 + …)?
8. 8.What is 58²? =
9. 9.What is √1521? =
10. 10.How many whole numbers lie between 16² and 17²?
11. 11.What is 97²? =
12. 12.Which of these is a perfect square? (a) 248 (b) 236 (c) 225
13. 13.What is 83²? =
14. 14.What is the sum of the first 5 odd numbers (1 + 3 + 5 + …)?
15. 15.What is the sum of the first 9 odd numbers (1 + 3 + 5 + …)?
16. 16.What is √400? =
17. 17.What is 25²? =
18. 18.How many whole numbers lie between 46² and 47²?
19. 19.What is 29²? =
20. 20.What is √6400? =
21. 21.A square garden has an area of 324 square m. How long is each side (in m)?
22. 22.What is 66²? =
23. 23.How many whole numbers lie between 35² and 36²?
24. 24.What is 85²? =
25. 25.What is the sum of the first 15 odd numbers (1 + 3 + 5 + …)?
26. 26.What is 30²? =
27. 27.What is √1225? =
28. 28.What is the sum of the first 18 odd numbers (1 + 3 + 5 + …)?
29. 29.What is √5041? =
30. 30.What is 86²? =
31. 31.How many whole numbers lie between 40² and 41²?
32. 32.How many whole numbers lie between 49² and 50²?
33. 33.What is the smallest whole number by which 810 must be multiplied to get a perfect square?
34. 34.A square garden has an area of 196 square m. How long is each side (in m)?
35. 35.Which of these is a perfect square? (a) 574 (b) 529 (c) 547
36. 36.What is 18²? =
37. 37.What is 94²? =
38. 38.How many whole numbers lie between 5² and 6²?
39. 39.What is the sum of the first 17 odd numbers (1 + 3 + 5 + …)?
40. 40.A square garden has an area of 144 square m. How long is each side (in m)?

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