Class 8 Maths Worksheet: Squares and Square Roots

Maths worksheets lesson 58: Squares and square roots · Set 88 · 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.How many whole numbers lie between 11² and 12²?
2. 2.What is the smallest whole number by which 27 must be divided to get a perfect square?
3. 3.Which of these is a perfect square? (a) 121 (b) 131 (c) 126
4. 4.What is the sum of the first 29 odd numbers (1 + 3 + 5 + …)?
5. 5.How many whole numbers lie between 49² and 50²?
6. 6.Which of these is a perfect square? (a) 109 (b) 100 (c) 112
7. 7.What is √7921? =
8. 8.What is √3600? =
9. 9.What is 61²? =
10. 10.How many whole numbers lie between 43² and 44²?
11. 11.A square garden has an area of 3481 square m. How long is each side (in m)?
12. 12.What is 31²? =
13. 13.What is the sum of the first 30 odd numbers (1 + 3 + 5 + …)?
14. 14.What is √529? =
15. 15.What is 98²? =
16. 16.What is the smallest whole number by which 160 must be multiplied to get a perfect square?
17. 17.What is √841? =
18. 18.What is the sum of the first 13 odd numbers (1 + 3 + 5 + …)?
19. 19.Which of these is a perfect square? (a) 1584 (b) 1521 (c) 1544
20. 20.What is 17²? =
21. 21.What is √4356? =
22. 22.What is 78²? =
23. 23.A square garden has an area of 484 square m. How long is each side (in m)?
24. 24.Which of these is a perfect square? (a) 1388 (b) 1369 (c) 1387
25. 25.What is 90²? =
26. 26.How many whole numbers lie between 25² and 26²?
27. 27.How many whole numbers lie between 37² and 38²?
28. 28.What is √1936? =
29. 29.A square garden has an area of 1764 square m. How long is each side (in m)?
30. 30.What is √7225? =
31. 31.What is the sum of the first 28 odd numbers (1 + 3 + 5 + …)?
32. 32.Which of these is a perfect square? (a) 951 (b) 900 (c) 912
33. 33.What is 52²? =
34. 34.What is the smallest whole number by which 320 must be divided to get a perfect square?
35. 35.What is the sum of the first 11 odd numbers (1 + 3 + 5 + …)?
36. 36.What is 37²? =
37. 37.What is the sum of the first 17 odd numbers (1 + 3 + 5 + …)?
38. 38.A square garden has an area of 625 square m. How long is each side (in m)?
39. 39.How many whole numbers lie between 40² and 41²?
40. 40.A square garden has an area of 841 square m. How long is each side (in m)?

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