Class 8 Maths Worksheet: Squares and Square Roots

Maths worksheets lesson 58: Squares and square roots · Set 44 · 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.A square garden has an area of 841 square m. How long is each side (in m)?
2. 2.How many whole numbers lie between 15² and 16²?
3. 3.Which of these is a perfect square? (a) 1369 (b) 1394 (c) 1393
4. 4.What is 62²? =
5. 5.Which of these is a perfect square? (a) 500 (b) 484 (c) 522
6. 6.What is 39²? =
7. 7.What is 73²? =
8. 8.What is the smallest whole number by which 243 must be divided to get a perfect square?
9. 9.Which of these is a perfect square? (a) 1606 (b) 1600 (c) 1627
10. 10.What is √1296? =
11. 11.What is √3844? =
12. 12.What is √6889? =
13. 13.What is √121? =
14. 14.What is the sum of the first 6 odd numbers (1 + 3 + 5 + …)?
15. 15.What is the smallest whole number by which 504 must be multiplied to get a perfect square?
16. 16.What is √1764? =
17. 17.What is the sum of the first 24 odd numbers (1 + 3 + 5 + …)?
18. 18.What is √6561? =
19. 19.What is 16²? =
20. 20.What is 89²? =
21. 21.What is the smallest whole number by which 384 must be multiplied to get a perfect square?
22. 22.How many whole numbers lie between 18² and 19²?
23. 23.What is 77²? =
24. 24.What is 65²? =
25. 25.What is the smallest whole number by which 27 must be multiplied to get a perfect square?
26. 26.How many whole numbers lie between 13² and 14²?
27. 27.What is 68²? =
28. 28.What is 97²? =
29. 29.What is 76²? =
30. 30.What is √324? =
31. 31.How many whole numbers lie between 12² and 13²?
32. 32.What is the sum of the first 11 odd numbers (1 + 3 + 5 + …)?
33. 33.A square garden has an area of 256 square m. How long is each side (in m)?
34. 34.Which of these is a perfect square? (a) 225 (b) 231 (c) 235
35. 35.What is 48²? =
36. 36.What is √8100? =
37. 37.What is the sum of the first 30 odd numbers (1 + 3 + 5 + …)?
38. 38.What is 95²? =
39. 39.What is the smallest whole number by which 180 must be divided to get a perfect square?
40. 40.What is √196? =

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