Class 8 Maths Worksheet: Squares and Square Roots

Maths worksheets lesson 58: Squares and square roots · Set 521 · 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 15²? =
2. 2.What is the sum of the first 12 odd numbers (1 + 3 + 5 + …)?
3. 3.How many whole numbers lie between 29² and 30²?
4. 4.What is 64²? =
5. 5.What is the sum of the first 30 odd numbers (1 + 3 + 5 + …)?
6. 6.What is the smallest whole number by which 405 must be divided to get a perfect square?
7. 7.What is the smallest whole number by which 539 must be multiplied to get a perfect square?
8. 8.What is √1369? =
9. 9.A square garden has an area of 441 square m. How long is each side (in m)?
10. 10.Which of these is a perfect square? (a) 1592 (b) 1521 (c) 1541
11. 11.What is √6889? =
12. 12.Which of these is a perfect square? (a) 453 (b) 441 (c) 460
13. 13.What is 79²? =
14. 14.What is 41²? =
15. 15.How many whole numbers lie between 37² and 38²?
16. 16.What is the smallest whole number by which 24 must be multiplied to get a perfect square?
17. 17.What is √5041? =
18. 18.A square garden has an area of 1681 square m. How long is each side (in m)?
19. 19.What is the sum of the first 19 odd numbers (1 + 3 + 5 + …)?
20. 20.What is the sum of the first 27 odd numbers (1 + 3 + 5 + …)?
21. 21.What is the smallest whole number by which 54 must be divided to get a perfect square?
22. 22.What is 28²? =
23. 23.How many whole numbers lie between 15² and 16²?
24. 24.What is 44²? =
25. 25.What is √784? =
26. 26.What is √289? =
27. 27.A square garden has an area of 2704 square m. How long is each side (in m)?
28. 28.What is 29²? =
29. 29.Which of these is a perfect square? (a) 493 (b) 488 (c) 484
30. 30.What is the smallest whole number by which 45 must be multiplied to get a perfect square?
31. 31.What is the sum of the first 8 odd numbers (1 + 3 + 5 + …)?
32. 32.A square garden has an area of 484 square m. How long is each side (in m)?
33. 33.What is the sum of the first 29 odd numbers (1 + 3 + 5 + …)?
34. 34.What is the sum of the first 11 odd numbers (1 + 3 + 5 + …)?
35. 35.What is 46²? =
36. 36.What is the smallest whole number by which 8 must be divided to get a perfect square?
37. 37.How many whole numbers lie between 32² and 33²?
38. 38.How many whole numbers lie between 26² and 27²?
39. 39.What is the sum of the first 16 odd numbers (1 + 3 + 5 + …)?
40. 40.What is √4624? =

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