Class 8 Maths Worksheet: Squares and Square Roots

Maths worksheets lesson 58: Squares and square roots · Set 161 · 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 18 odd numbers (1 + 3 + 5 + …)?
2. 2.How many whole numbers lie between 19² and 20²?
3. 3.What is the sum of the first 19 odd numbers (1 + 3 + 5 + …)?
4. 4.What is √484? =
5. 5.Which of these is a perfect square? (a) 163 (b) 160 (c) 144
6. 6.What is the sum of the first 15 odd numbers (1 + 3 + 5 + …)?
7. 7.What is the sum of the first 11 odd numbers (1 + 3 + 5 + …)?
8. 8.What is the sum of the first 8 odd numbers (1 + 3 + 5 + …)?
9. 9.How many whole numbers lie between 42² and 43²?
10. 10.What is √900? =
11. 11.What is √576? =
12. 12.What is the sum of the first 6 odd numbers (1 + 3 + 5 + …)?
13. 13.What is the smallest whole number by which 125 must be divided to get a perfect square?
14. 14.What is √5329? =
15. 15.How many whole numbers lie between 21² and 22²?
16. 16.Which of these is a perfect square? (a) 224 (b) 197 (c) 196
17. 17.What is 14²? =
18. 18.What is √7396? =
19. 19.What is 69²? =
20. 20.Which of these is a perfect square? (a) 755 (b) 729 (c) 763
21. 21.What is 93²? =
22. 22.What is the sum of the first 14 odd numbers (1 + 3 + 5 + …)?
23. 23.How many whole numbers lie between 22² and 23²?
24. 24.A square garden has an area of 121 square m. How long is each side (in m)?
25. 25.What is √1444? =
26. 26.What is 87²? =
27. 27.How many whole numbers lie between 15² and 16²?
28. 28.How many whole numbers lie between 35² and 36²?
29. 29.A square garden has an area of 2500 square m. How long is each side (in m)?
30. 30.How many whole numbers lie between 43² and 44²?
31. 31.How many whole numbers lie between 47² and 48²?
32. 32.Which of these is a perfect square? (a) 1024 (b) 1029 (c) 1083
33. 33.What is the smallest whole number by which 20 must be multiplied to get a perfect square?
34. 34.Which of these is a perfect square? (a) 1521 (b) 1523 (c) 1534
35. 35.What is 11²? =
36. 36.What is the smallest whole number by which 832 must be divided to get a perfect square?
37. 37.What is the sum of the first 9 odd numbers (1 + 3 + 5 + …)?
38. 38.How many whole numbers lie between 33² and 34²?
39. 39.A square garden has an area of 196 square m. How long is each side (in m)?
40. 40.How many whole numbers lie between 49² and 50²?

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