Class 8 Maths Worksheet: Squares and Square Roots

Maths worksheets lesson 58: Squares and square roots · Set 653 · 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) 271 (b) 257 (c) 256
2. 2.What is 19²? =
3. 3.What is 24²? =
4. 4.What is the smallest whole number by which 504 must be divided to get a perfect square?
5. 5.A square garden has an area of 121 square m. How long is each side (in m)?
6. 6.What is √1681? =
7. 7.How many whole numbers lie between 28² and 29²?
8. 8.What is √1600? =
9. 9.How many whole numbers lie between 49² and 50²?
10. 10.What is the sum of the first 7 odd numbers (1 + 3 + 5 + …)?
11. 11.What is √1936? =
12. 12.What is the smallest whole number by which 396 must be divided to get a perfect square?
13. 13.What is the smallest whole number by which 637 must be multiplied to get a perfect square?
14. 14.A square garden has an area of 1444 square m. How long is each side (in m)?
15. 15.How many whole numbers lie between 43² and 44²?
16. 16.Which of these is a perfect square? (a) 676 (b) 722 (c) 724
17. 17.Which of these is a perfect square? (a) 336 (b) 353 (c) 324
18. 18.What is 17²? =
19. 19.What is 95²? =
20. 20.What is 72²? =
21. 21.What is 42²? =
22. 22.How many whole numbers lie between 42² and 43²?
23. 23.A square garden has an area of 36 square m. How long is each side (in m)?
24. 24.What is the smallest whole number by which 252 must be multiplied to get a perfect square?
25. 25.What is 11²? =
26. 26.What is √9409? =
27. 27.A square garden has an area of 49 square m. How long is each side (in m)?
28. 28.What is the smallest whole number by which 18 must be divided to get a perfect square?
29. 29.What is the smallest whole number by which 72 must be multiplied to get a perfect square?
30. 30.What is √361? =
31. 31.What is the smallest whole number by which 637 must be divided to get a perfect square?
32. 32.What is 51²? =
33. 33.A square garden has an area of 1369 square m. How long is each side (in m)?
34. 34.A square garden has an area of 1764 square m. How long is each side (in m)?
35. 35.What is 27²? =
36. 36.Which of these is a perfect square? (a) 955 (b) 900 (c) 901
37. 37.What is the sum of the first 30 odd numbers (1 + 3 + 5 + …)?
38. 38.How many whole numbers lie between 37² and 38²?
39. 39.What is the sum of the first 19 odd numbers (1 + 3 + 5 + …)?
40. 40.How many whole numbers lie between 16² and 17²?

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