Class 8 Maths Worksheet: Squares and Square Roots

Maths worksheets lesson 58: Squares and square roots · Set 316 · 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 23 odd numbers (1 + 3 + 5 + …)?
2. 2.A square garden has an area of 81 square m. How long is each side (in m)?
3. 3.What is 46²? =
4. 4.What is the sum of the first 29 odd numbers (1 + 3 + 5 + …)?
5. 5.What is the sum of the first 28 odd numbers (1 + 3 + 5 + …)?
6. 6.How many whole numbers lie between 35² and 36²?
7. 7.What is the smallest whole number by which 12 must be multiplied to get a perfect square?
8. 8.What is the sum of the first 20 odd numbers (1 + 3 + 5 + …)?
9. 9.What is 16²? =
10. 10.What is the sum of the first 30 odd numbers (1 + 3 + 5 + …)?
11. 11.What is 80²? =
12. 12.What is 31²? =
13. 13.What is √7569? =
14. 14.What is √169? =
15. 15.How many whole numbers lie between 37² and 38²?
16. 16.What is the smallest whole number by which 27 must be divided to get a perfect square?
17. 17.What is the smallest whole number by which 896 must be divided to get a perfect square?
18. 18.What is the sum of the first 25 odd numbers (1 + 3 + 5 + …)?
19. 19.What is √144? =
20. 20.What is √4900? =
21. 21.A square garden has an area of 1296 square m. How long is each side (in m)?
22. 22.A square garden has an area of 289 square m. How long is each side (in m)?
23. 23.How many whole numbers lie between 27² and 28²?
24. 24.What is the sum of the first 13 odd numbers (1 + 3 + 5 + …)?
25. 25.What is √2704? =
26. 26.How many whole numbers lie between 36² and 37²?
27. 27.What is the smallest whole number by which 486 must be multiplied to get a perfect square?
28. 28.A square garden has an area of 1089 square m. How long is each side (in m)?
29. 29.What is the smallest whole number by which 343 must be divided to get a perfect square?
30. 30.What is √7921? =
31. 31.Which of these is a perfect square? (a) 121 (b) 137 (c) 131
32. 32.What is 53²? =
33. 33.What is 67²? =
34. 34.A square garden has an area of 3249 square m. How long is each side (in m)?
35. 35.How many whole numbers lie between 18² and 19²?
36. 36.What is √6561? =
37. 37.A square garden has an area of 1369 square m. How long is each side (in m)?
38. 38.A square garden has an area of 256 square m. How long is each side (in m)?
39. 39.What is the smallest whole number by which 1053 must be divided to get a perfect square?
40. 40.What is √9604? =

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