Class 8 Maths Worksheet: Squares and Square Roots

Maths worksheets lesson 58: Squares and square roots · Set 293 · 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.Which of these is a perfect square? (a) 1168 (b) 1219 (c) 1156
2. 2.What is 28²? =
3. 3.What is 92²? =
4. 4.A square garden has an area of 324 square m. How long is each side (in m)?
5. 5.How many whole numbers lie between 40² and 41²?
6. 6.A square garden has an area of 36 square m. How long is each side (in m)?
7. 7.What is √4624? =
8. 8.How many whole numbers lie between 9² and 10²?
9. 9.What is √3721? =
10. 10.What is 29²? =
11. 11.What is 32²? =
12. 12.What is 14²? =
13. 13.A square garden has an area of 3249 square m. How long is each side (in m)?
14. 14.What is the smallest whole number by which 275 must be multiplied to get a perfect square?
15. 15.What is the smallest whole number by which 40 must be multiplied to get a perfect square?
16. 16.How many whole numbers lie between 16² and 17²?
17. 17.What is the smallest whole number by which 98 must be multiplied to get a perfect square?
18. 18.What is 88²? =
19. 19.Which of these is a perfect square? (a) 308 (b) 291 (c) 289
20. 20.What is 77²? =
21. 21.How many whole numbers lie between 45² and 46²?
22. 22.A square garden has an area of 2601 square m. How long is each side (in m)?
23. 23.Which of these is a perfect square? (a) 324 (b) 351 (c) 327
24. 24.What is √5776? =
25. 25.What is the smallest whole number by which 126 must be multiplied to get a perfect square?
26. 26.What is the sum of the first 15 odd numbers (1 + 3 + 5 + …)?
27. 27.A square garden has an area of 196 square m. How long is each side (in m)?
28. 28.What is √1849? =
29. 29.A square garden has an area of 441 square m. How long is each side (in m)?
30. 30.A square garden has an area of 1089 square m. How long is each side (in m)?
31. 31.What is the smallest whole number by which 275 must be divided to get a perfect square?
32. 32.How many whole numbers lie between 18² and 19²?
33. 33.What is 69²? =
34. 34.What is the smallest whole number by which 108 must be multiplied to get a perfect square?
35. 35.How many whole numbers lie between 30² and 31²?
36. 36.What is 68²? =
37. 37.What is √1764? =
38. 38.What is 75²? =
39. 39.What is the smallest whole number by which 28 must be multiplied to get a perfect square?
40. 40.What is 49²? =

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