Class 8 Maths Worksheet: Squares and Square Roots

Maths worksheets lesson 58: Squares and square roots · Set 268 · 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 80 must be multiplied to get a perfect square?
2. 2.What is 95²? =
3. 3.What is 28²? =
4. 4.What is the sum of the first 18 odd numbers (1 + 3 + 5 + …)?
5. 5.How many whole numbers lie between 39² and 40²?
6. 6.How many whole numbers lie between 47² and 48²?
7. 7.Which of these is a perfect square? (a) 686 (b) 676 (c) 684
8. 8.What is √7921? =
9. 9.Which of these is a perfect square? (a) 528 (b) 484 (c) 505
10. 10.What is the smallest whole number by which 175 must be multiplied to get a perfect square?
11. 11.What is the smallest whole number by which 45 must be multiplied to get a perfect square?
12. 12.What is √6889? =
13. 13.How many whole numbers lie between 6² and 7²?
14. 14.Which of these is a perfect square? (a) 1510 (b) 1474 (c) 1444
15. 15.Which of these is a perfect square? (a) 1521 (b) 1595 (c) 1588
16. 16.How many whole numbers lie between 34² and 35²?
17. 17.What is √1849? =
18. 18.How many whole numbers lie between 38² and 39²?
19. 19.What is √6724? =
20. 20.How many whole numbers lie between 11² and 12²?
21. 21.How many whole numbers lie between 35² and 36²?
22. 22.How many whole numbers lie between 13² and 14²?
23. 23.What is 88²? =
24. 24.A square garden has an area of 961 square m. How long is each side (in m)?
25. 25.What is √7744? =
26. 26.What is 66²? =
27. 27.What is the sum of the first 30 odd numbers (1 + 3 + 5 + …)?
28. 28.Which of these is a perfect square? (a) 1261 (b) 1259 (c) 1225
29. 29.A square garden has an area of 1225 square m. How long is each side (in m)?
30. 30.What is the sum of the first 24 odd numbers (1 + 3 + 5 + …)?
31. 31.What is √441? =
32. 32.What is 43²? =
33. 33.What is 37²? =
34. 34.What is 69²? =
35. 35.What is the sum of the first 15 odd numbers (1 + 3 + 5 + …)?
36. 36.What is the sum of the first 26 odd numbers (1 + 3 + 5 + …)?
37. 37.What is 12²? =
38. 38.What is the smallest whole number by which 96 must be multiplied to get a perfect square?
39. 39.Which of these is a perfect square? (a) 333 (b) 324 (c) 336
40. 40.What is the sum of the first 12 odd numbers (1 + 3 + 5 + …)?

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