Class 8 Maths Worksheet: Squares and Square Roots

Maths worksheets lesson 58: Squares and square roots · Set 690 · 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 89²? =
2. 2.A square garden has an area of 3600 square m. How long is each side (in m)?
3. 3.What is the sum of the first 8 odd numbers (1 + 3 + 5 + …)?
4. 4.What is 84²? =
5. 5.What is √2116? =
6. 6.What is the smallest whole number by which 540 must be multiplied to get a perfect square?
7. 7.What is 70²? =
8. 8.What is √625? =
9. 9.Which of these is a perfect square? (a) 484 (b) 510 (c) 492
10. 10.What is 61²? =
11. 11.What is √3025? =
12. 12.How many whole numbers lie between 48² and 49²?
13. 13.What is 12²? =
14. 14.Which of these is a perfect square? (a) 169 (b) 192 (c) 184
15. 15.Which of these is a perfect square? (a) 1156 (b) 1182 (c) 1200
16. 16.Which of these is a perfect square? (a) 132 (b) 121 (c) 128
17. 17.What is the smallest whole number by which 375 must be divided to get a perfect square?
18. 18.A square garden has an area of 1089 square m. How long is each side (in m)?
19. 19.How many whole numbers lie between 11² and 12²?
20. 20.What is 36²? =
21. 21.What is 88²? =
22. 22.What is 90²? =
23. 23.What is 35²? =
24. 24.A square garden has an area of 1225 square m. How long is each side (in m)?
25. 25.What is the smallest whole number by which 243 must be multiplied to get a perfect square?
26. 26.What is the smallest whole number by which 99 must be divided to get a perfect square?
27. 27.What is 21²? =
28. 28.What is √4489? =
29. 29.What is 65²? =
30. 30.What is the sum of the first 19 odd numbers (1 + 3 + 5 + …)?
31. 31.What is the smallest whole number by which 275 must be divided to get a perfect square?
32. 32.What is √289? =
33. 33.How many whole numbers lie between 41² and 42²?
34. 34.What is the sum of the first 29 odd numbers (1 + 3 + 5 + …)?
35. 35.Which of these is a perfect square? (a) 117 (b) 108 (c) 100
36. 36.Which of these is a perfect square? (a) 198 (b) 196 (c) 201
37. 37.Which of these is a perfect square? (a) 1225 (b) 1266 (c) 1235
38. 38.What is √6241? =
39. 39.What is the smallest whole number by which 150 must be multiplied to get a perfect square?
40. 40.What is 64²? =

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