Class 8 Maths Worksheet: Squares and Square Roots

Maths worksheets lesson 58: Squares and square roots · Set 226 · 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 34² and 35²?
2. 2.What is the smallest whole number by which 810 must be divided to get a perfect square?
3. 3.What is 80²? =
4. 4.A square garden has an area of 289 square m. How long is each side (in m)?
5. 5.A square garden has an area of 3481 square m. How long is each side (in m)?
6. 6.A square garden has an area of 36 square m. How long is each side (in m)?
7. 7.What is the sum of the first 10 odd numbers (1 + 3 + 5 + …)?
8. 8.What is the smallest whole number by which 375 must be multiplied to get a perfect square?
9. 9.How many whole numbers lie between 48² and 49²?
10. 10.What is 12²? =
11. 11.What is the sum of the first 13 odd numbers (1 + 3 + 5 + …)?
12. 12.What is 52²? =
13. 13.What is 22²? =
14. 14.What is the sum of the first 8 odd numbers (1 + 3 + 5 + …)?
15. 15.A square garden has an area of 3136 square m. How long is each side (in m)?
16. 16.What is the smallest whole number by which 504 must be multiplied to get a perfect square?
17. 17.How many whole numbers lie between 8² and 9²?
18. 18.Which of these is a perfect square? (a) 205 (b) 196 (c) 215
19. 19.What is 71²? =
20. 20.How many whole numbers lie between 15² and 16²?
21. 21.What is √7744? =
22. 22.What is 87²? =
23. 23.What is √121? =
24. 24.What is √4356? =
25. 25.What is the sum of the first 25 odd numbers (1 + 3 + 5 + …)?
26. 26.Which of these is a perfect square? (a) 1216 (b) 1156 (c) 1207
27. 27.What is 83²? =
28. 28.What is √1764? =
29. 29.What is the sum of the first 22 odd numbers (1 + 3 + 5 + …)?
30. 30.A square garden has an area of 324 square m. How long is each side (in m)?
31. 31.What is the smallest whole number by which 24 must be multiplied to get a perfect square?
32. 32.What is the sum of the first 11 odd numbers (1 + 3 + 5 + …)?
33. 33.Which of these is a perfect square? (a) 503 (b) 484 (c) 488
34. 34.Which of these is a perfect square? (a) 576 (b) 586 (c) 588
35. 35.A square garden has an area of 121 square m. How long is each side (in m)?
36. 36.How many whole numbers lie between 32² and 33²?
37. 37.A square garden has an area of 64 square m. How long is each side (in m)?
38. 38.How many whole numbers lie between 28² and 29²?
39. 39.What is the sum of the first 28 odd numbers (1 + 3 + 5 + …)?
40. 40.How many whole numbers lie between 46² and 47²?

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