Class 8 Maths Worksheet: Squares and Square Roots

Maths worksheets lesson 58: Squares and square roots · Set 369 · 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) 1156 (b) 1212 (c) 1198
2. 2.How many whole numbers lie between 30² and 31²?
3. 3.Which of these is a perfect square? (a) 186 (b) 169 (c) 195
4. 4.What is the smallest whole number by which 325 must be divided to get a perfect square?
5. 5.What is 16²? =
6. 6.What is √961? =
7. 7.How many whole numbers lie between 5² and 6²?
8. 8.What is √576? =
9. 9.What is √1764? =
10. 10.A square garden has an area of 1225 square m. How long is each side (in m)?
11. 11.Which of these is a perfect square? (a) 324 (b) 331 (c) 345
12. 12.How many whole numbers lie between 17² and 18²?
13. 13.What is 69²? =
14. 14.How many whole numbers lie between 8² and 9²?
15. 15.Which of these is a perfect square? (a) 1675 (b) 1627 (c) 1600
16. 16.Which of these is a perfect square? (a) 973 (b) 991 (c) 961
17. 17.How many whole numbers lie between 40² and 41²?
18. 18.What is the smallest whole number by which 96 must be multiplied to get a perfect square?
19. 19.What is √289? =
20. 20.A square garden has an area of 289 square m. How long is each side (in m)?
21. 21.What is 70²? =
22. 22.What is the sum of the first 9 odd numbers (1 + 3 + 5 + …)?
23. 23.What is the sum of the first 15 odd numbers (1 + 3 + 5 + …)?
24. 24.What is √2601? =
25. 25.What is 63²? =
26. 26.What is √2500? =
27. 27.What is √5041? =
28. 28.What is the smallest whole number by which 504 must be multiplied to get a perfect square?
29. 29.A square garden has an area of 3364 square m. How long is each side (in m)?
30. 30.How many whole numbers lie between 45² and 46²?
31. 31.How many whole numbers lie between 41² and 42²?
32. 32.How many whole numbers lie between 36² and 37²?
33. 33.Which of these is a perfect square? (a) 900 (b) 912 (c) 943
34. 34.A square garden has an area of 1764 square m. How long is each side (in m)?
35. 35.What is the smallest whole number by which 50 must be divided to get a perfect square?
36. 36.What is the smallest whole number by which 28 must be divided to get a perfect square?
37. 37.Which of these is a perfect square? (a) 100 (b) 104 (c) 120
38. 38.What is √8281? =
39. 39.How many whole numbers lie between 37² and 38²?
40. 40.What is 59²? =

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