Class 8 Maths Worksheet: Squares and Square Roots

Maths worksheets lesson 58: Squares and square roots · Set 7 · 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 the smallest whole number by which 40 must be multiplied to get a perfect square?
2. 2.A square garden has an area of 729 square m. How long is each side (in m)?
3. 3.What is the sum of the first 17 odd numbers (1 + 3 + 5 + …)?
4. 4.How many whole numbers lie between 6² and 7²?
5. 5.What is √6241? =
6. 6.Which of these is a perfect square? (a) 1119 (b) 1122 (c) 1089
7. 7.How many whole numbers lie between 26² and 27²?
8. 8.How many whole numbers lie between 42² and 43²?
9. 9.What is the sum of the first 15 odd numbers (1 + 3 + 5 + …)?
10. 10.What is 48²? =
11. 11.What is √841? =
12. 12.How many whole numbers lie between 50² and 51²?
13. 13.What is the sum of the first 6 odd numbers (1 + 3 + 5 + …)?
14. 14.Which of these is a perfect square? (a) 1453 (b) 1444 (c) 1501
15. 15.What is 90²? =
16. 16.A square garden has an area of 441 square m. How long is each side (in m)?
17. 17.What is the smallest whole number by which 891 must be divided to get a perfect square?
18. 18.How many whole numbers lie between 33² and 34²?
19. 19.What is the sum of the first 20 odd numbers (1 + 3 + 5 + …)?
20. 20.What is the sum of the first 23 odd numbers (1 + 3 + 5 + …)?
21. 21.What is √2809? =
22. 22.What is the sum of the first 11 odd numbers (1 + 3 + 5 + …)?
23. 23.What is √289? =
24. 24.How many whole numbers lie between 21² and 22²?
25. 25.What is 17²? =
26. 26.What is the smallest whole number by which 468 must be multiplied to get a perfect square?
27. 27.What is the smallest whole number by which 384 must be multiplied to get a perfect square?
28. 28.What is the sum of the first 22 odd numbers (1 + 3 + 5 + …)?
29. 29.What is √1296? =
30. 30.How many whole numbers lie between 40² and 41²?
31. 31.How many whole numbers lie between 13² and 14²?
32. 32.Which of these is a perfect square? (a) 646 (b) 625 (c) 652
33. 33.What is the sum of the first 19 odd numbers (1 + 3 + 5 + …)?
34. 34.How many whole numbers lie between 5² and 6²?
35. 35.What is the sum of the first 9 odd numbers (1 + 3 + 5 + …)?
36. 36.What is √4624? =
37. 37.What is √4900? =
38. 38.What is √3600? =
39. 39.What is the sum of the first 16 odd numbers (1 + 3 + 5 + …)?
40. 40.A square garden has an area of 2116 square m. How long is each side (in m)?

Free maths worksheets lessons, practice and worksheets at talentjr.in/maths-worksheets