Class 8 Maths Worksheet: Squares and Square Roots

Maths worksheets lesson 58: Squares and square roots · Set 473 · 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 8 must be multiplied to get a perfect square?
2. 2.What is the sum of the first 28 odd numbers (1 + 3 + 5 + …)?
3. 3.What is the sum of the first 25 odd numbers (1 + 3 + 5 + …)?
4. 4.What is the sum of the first 30 odd numbers (1 + 3 + 5 + …)?
5. 5.How many whole numbers lie between 16² and 17²?
6. 6.What is 84²? =
7. 7.Which of these is a perfect square? (a) 590 (b) 603 (c) 576
8. 8.What is 76²? =
9. 9.What is 57²? =
10. 10.A square garden has an area of 2916 square m. How long is each side (in m)?
11. 11.What is 33²? =
12. 12.What is the sum of the first 10 odd numbers (1 + 3 + 5 + …)?
13. 13.What is 55²? =
14. 14.Which of these is a perfect square? (a) 502 (b) 484 (c) 495
15. 15.What is 99²? =
16. 16.How many whole numbers lie between 25² and 26²?
17. 17.What is the sum of the first 29 odd numbers (1 + 3 + 5 + …)?
18. 18.Which of these is a perfect square? (a) 225 (b) 252 (c) 254
19. 19.A square garden has an area of 625 square m. How long is each side (in m)?
20. 20.What is the sum of the first 15 odd numbers (1 + 3 + 5 + …)?
21. 21.What is 64²? =
22. 22.What is the smallest whole number by which 98 must be multiplied to get a perfect square?
23. 23.Which of these is a perfect square? (a) 263 (b) 256 (c) 258
24. 24.How many whole numbers lie between 22² and 23²?
25. 25.What is the sum of the first 12 odd numbers (1 + 3 + 5 + …)?
26. 26.What is 62²? =
27. 27.A square garden has an area of 1089 square m. How long is each side (in m)?
28. 28.How many whole numbers lie between 12² and 13²?
29. 29.What is √7744? =
30. 30.What is 27²? =
31. 31.A square garden has an area of 2601 square m. How long is each side (in m)?
32. 32.What is the smallest whole number by which 48 must be divided to get a perfect square?
33. 33.A square garden has an area of 121 square m. How long is each side (in m)?
34. 34.How many whole numbers lie between 34² and 35²?
35. 35.What is the sum of the first 17 odd numbers (1 + 3 + 5 + …)?
36. 36.How many whole numbers lie between 5² and 6²?
37. 37.What is 38²? =
38. 38.How many whole numbers lie between 13² and 14²?
39. 39.How many whole numbers lie between 32² and 33²?
40. 40.Which of these is a perfect square? (a) 1448 (b) 1485 (c) 1444

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