Class 8 Maths Worksheet: Squares and Square Roots

Maths worksheets lesson 58: Squares and square roots · Set 249 · 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 26²? =
2. 2.What is the sum of the first 12 odd numbers (1 + 3 + 5 + …)?
3. 3.What is the sum of the first 15 odd numbers (1 + 3 + 5 + …)?
4. 4.What is √3844? =
5. 5.What is the sum of the first 14 odd numbers (1 + 3 + 5 + …)?
6. 6.What is the sum of the first 5 odd numbers (1 + 3 + 5 + …)?
7. 7.Which of these is a perfect square? (a) 1272 (b) 1225 (c) 1238
8. 8.What is the sum of the first 22 odd numbers (1 + 3 + 5 + …)?
9. 9.What is the smallest whole number by which 1053 must be multiplied to get a perfect square?
10. 10.What is √3481? =
11. 11.A square garden has an area of 676 square m. How long is each side (in m)?
12. 12.What is the smallest whole number by which 350 must be divided to get a perfect square?
13. 13.Which of these is a perfect square? (a) 1315 (b) 1326 (c) 1296
14. 14.Which of these is a perfect square? (a) 396 (b) 383 (c) 361
15. 15.What is √2209? =
16. 16.A square garden has an area of 576 square m. How long is each side (in m)?
17. 17.Which of these is a perfect square? (a) 1089 (b) 1121 (c) 1122
18. 18.What is the sum of the first 13 odd numbers (1 + 3 + 5 + …)?
19. 19.What is the smallest whole number by which 54 must be multiplied to get a perfect square?
20. 20.A square garden has an area of 81 square m. How long is each side (in m)?
21. 21.What is 11²? =
22. 22.What is the smallest whole number by which 637 must be multiplied to get a perfect square?
23. 23.A square garden has an area of 289 square m. How long is each side (in m)?
24. 24.What is √8649? =
25. 25.What is 91²? =
26. 26.What is 80²? =
27. 27.What is the sum of the first 6 odd numbers (1 + 3 + 5 + …)?
28. 28.What is √1369? =
29. 29.What is the sum of the first 25 odd numbers (1 + 3 + 5 + …)?
30. 30.What is √7744? =
31. 31.What is the smallest whole number by which 490 must be divided to get a perfect square?
32. 32.What is 12²? =
33. 33.A square garden has an area of 2025 square m. How long is each side (in m)?
34. 34.What is 35²? =
35. 35.What is the sum of the first 17 odd numbers (1 + 3 + 5 + …)?
36. 36.What is the smallest whole number by which 128 must be multiplied to get a perfect square?
37. 37.How many whole numbers lie between 26² and 27²?
38. 38.How many whole numbers lie between 25² and 26²?
39. 39.What is 45²? =
40. 40.A square garden has an area of 121 square m. How long is each side (in m)?

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