Class 8 Maths Worksheet: Squares and Square Roots

Maths worksheets lesson 58: Squares and square roots · Set 713 · 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 91²? =
2. 2.Which of these is a perfect square? (a) 389 (b) 397 (c) 361
3. 3.What is 67²? =
4. 4.Which of these is a perfect square? (a) 1269 (b) 1294 (c) 1225
5. 5.What is 21²? =
6. 6.What is the smallest whole number by which 98 must be divided to get a perfect square?
7. 7.What is the smallest whole number by which 56 must be multiplied to get a perfect square?
8. 8.Which of these is a perfect square? (a) 242 (b) 252 (c) 225
9. 9.What is √784? =
10. 10.How many whole numbers lie between 25² and 26²?
11. 11.What is √225? =
12. 12.What is the sum of the first 18 odd numbers (1 + 3 + 5 + …)?
13. 13.What is √3136? =
14. 14.What is the sum of the first 30 odd numbers (1 + 3 + 5 + …)?
15. 15.What is 84²? =
16. 16.A square garden has an area of 36 square m. How long is each side (in m)?
17. 17.What is √4489? =
18. 18.Which of these is a perfect square? (a) 289 (b) 294 (c) 315
19. 19.A square garden has an area of 484 square m. How long is each side (in m)?
20. 20.What is √961? =
21. 21.What is 97²? =
22. 22.How many whole numbers lie between 39² and 40²?
23. 23.What is √5329? =
24. 24.What is the sum of the first 7 odd numbers (1 + 3 + 5 + …)?
25. 25.What is √4624? =
26. 26.What is the smallest whole number by which 117 must be divided to get a perfect square?
27. 27.How many whole numbers lie between 34² and 35²?
28. 28.A square garden has an area of 196 square m. How long is each side (in m)?
29. 29.How many whole numbers lie between 38² and 39²?
30. 30.What is the smallest whole number by which 891 must be divided to get a perfect square?
31. 31.What is the smallest whole number by which 350 must be divided to get a perfect square?
32. 32.Which of these is a perfect square? (a) 144 (b) 152 (c) 149
33. 33.A square garden has an area of 144 square m. How long is each side (in m)?
34. 34.A square garden has an area of 25 square m. How long is each side (in m)?
35. 35.A square garden has an area of 529 square m. How long is each side (in m)?
36. 36.What is 64²? =
37. 37.What is 77²? =
38. 38.What is the smallest whole number by which 243 must be divided to get a perfect square?
39. 39.A square garden has an area of 1296 square m. How long is each side (in m)?
40. 40.How many whole numbers lie between 5² and 6²?

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