Class 8 Maths Worksheet: Squares and Square Roots

Maths worksheets lesson 58: Squares and square roots · Set 623 · 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 sum of the first 5 odd numbers (1 + 3 + 5 + …)?
2. 2.How many whole numbers lie between 33² and 34²?
3. 3.Which of these is a perfect square? (a) 729 (b) 757 (c) 763
4. 4.What is the smallest whole number by which 24 must be divided to get a perfect square?
5. 5.What is the sum of the first 8 odd numbers (1 + 3 + 5 + …)?
6. 6.What is the sum of the first 19 odd numbers (1 + 3 + 5 + …)?
7. 7.A square garden has an area of 2601 square m. How long is each side (in m)?
8. 8.What is the smallest whole number by which 405 must be divided to get a perfect square?
9. 9.What is 33²? =
10. 10.What is √4624? =
11. 11.What is √529? =
12. 12.How many whole numbers lie between 19² and 20²?
13. 13.A square garden has an area of 3249 square m. How long is each side (in m)?
14. 14.Which of these is a perfect square? (a) 1024 (b) 1081 (c) 1079
15. 15.A square garden has an area of 2209 square m. How long is each side (in m)?
16. 16.What is √1936? =
17. 17.What is the smallest whole number by which 18 must be multiplied to get a perfect square?
18. 18.Which of these is a perfect square? (a) 532 (b) 529 (c) 568
19. 19.How many whole numbers lie between 34² and 35²?
20. 20.What is 25²? =
21. 21.What is the smallest whole number by which 448 must be multiplied to get a perfect square?
22. 22.A square garden has an area of 49 square m. How long is each side (in m)?
23. 23.What is the sum of the first 27 odd numbers (1 + 3 + 5 + …)?
24. 24.Which of these is a perfect square? (a) 1296 (b) 1318 (c) 1321
25. 25.What is 29²? =
26. 26.What is the smallest whole number by which 12 must be divided to get a perfect square?
27. 27.What is the smallest whole number by which 96 must be divided to get a perfect square?
28. 28.How many whole numbers lie between 39² and 40²?
29. 29.What is the sum of the first 18 odd numbers (1 + 3 + 5 + …)?
30. 30.What is the smallest whole number by which 810 must be multiplied to get a perfect square?
31. 31.Which of these is a perfect square? (a) 714 (b) 690 (c) 676
32. 32.What is √6724? =
33. 33.How many whole numbers lie between 12² and 13²?
34. 34.Which of these is a perfect square? (a) 625 (b) 674 (c) 627
35. 35.What is 62²? =
36. 36.What is 22²? =
37. 37.What is 21²? =
38. 38.What is the sum of the first 21 odd numbers (1 + 3 + 5 + …)?
39. 39.What is 92²? =
40. 40.What is 89²? =

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