Class 8 Maths Worksheet: Squares and Square Roots

Maths worksheets lesson 58: Squares and square roots · Set 528 · 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 78²? =
2. 2.A square garden has an area of 100 square m. How long is each side (in m)?
3. 3.How many whole numbers lie between 34² and 35²?
4. 4.How many whole numbers lie between 21² and 22²?
5. 5.What is the sum of the first 6 odd numbers (1 + 3 + 5 + …)?
6. 6.What is the smallest whole number by which 350 must be multiplied to get a perfect square?
7. 7.How many whole numbers lie between 48² and 49²?
8. 8.What is 18²? =
9. 9.What is the sum of the first 29 odd numbers (1 + 3 + 5 + …)?
10. 10.What is √9604? =
11. 11.Which of these is a perfect square? (a) 327 (b) 324 (c) 347
12. 12.What is √361? =
13. 13.What is 45²? =
14. 14.What is 11²? =
15. 15.What is √1089? =
16. 16.What is √729? =
17. 17.How many whole numbers lie between 29² and 30²?
18. 18.A square garden has an area of 256 square m. How long is each side (in m)?
19. 19.What is the smallest whole number by which 960 must be multiplied to get a perfect square?
20. 20.What is 96²? =
21. 21.What is the sum of the first 7 odd numbers (1 + 3 + 5 + …)?
22. 22.What is the smallest whole number by which 294 must be divided to get a perfect square?
23. 23.What is the sum of the first 17 odd numbers (1 + 3 + 5 + …)?
24. 24.A square garden has an area of 2025 square m. How long is each side (in m)?
25. 25.What is the sum of the first 20 odd numbers (1 + 3 + 5 + …)?
26. 26.A square garden has an area of 49 square m. How long is each side (in m)?
27. 27.What is √256? =
28. 28.What is √3844? =
29. 29.What is the smallest whole number by which 44 must be divided to get a perfect square?
30. 30.Which of these is a perfect square? (a) 100 (b) 109 (c) 104
31. 31.What is √900? =
32. 32.What is 91²? =
33. 33.What is the sum of the first 25 odd numbers (1 + 3 + 5 + …)?
34. 34.A square garden has an area of 900 square m. How long is each side (in m)?
35. 35.What is 44²? =
36. 36.What is √1225? =
37. 37.What is √2025? =
38. 38.A square garden has an area of 576 square m. How long is each side (in m)?
39. 39.What is √4356? =
40. 40.What is √1849? =

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