Class 8 Maths Worksheet: Squares and Square Roots

Maths worksheets lesson 58: Squares and square roots · Set 280 · 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.A square garden has an area of 2916 square m. How long is each side (in m)?
2. 2.What is √6561? =
3. 3.What is 65²? =
4. 4.What is the sum of the first 9 odd numbers (1 + 3 + 5 + …)?
5. 5.Which of these is a perfect square? (a) 1301 (b) 1334 (c) 1296
6. 6.What is the smallest whole number by which 54 must be divided to get a perfect square?
7. 7.What is √625? =
8. 8.What is the smallest whole number by which 539 must be multiplied to get a perfect square?
9. 9.What is the sum of the first 23 odd numbers (1 + 3 + 5 + …)?
10. 10.How many whole numbers lie between 39² and 40²?
11. 11.What is 26²? =
12. 12.A square garden has an area of 196 square m. How long is each side (in m)?
13. 13.How many whole numbers lie between 13² and 14²?
14. 14.How many whole numbers lie between 19² and 20²?
15. 15.What is √4761? =
16. 16.Which of these is a perfect square? (a) 1123 (b) 1089 (c) 1145
17. 17.Which of these is a perfect square? (a) 353 (b) 324 (c) 337
18. 18.What is the sum of the first 7 odd numbers (1 + 3 + 5 + …)?
19. 19.How many whole numbers lie between 10² and 11²?
20. 20.What is √4624? =
21. 21.Which of these is a perfect square? (a) 997 (b) 983 (c) 961
22. 22.A square garden has an area of 49 square m. How long is each side (in m)?
23. 23.How many whole numbers lie between 9² and 10²?
24. 24.A square garden has an area of 100 square m. How long is each side (in m)?
25. 25.What is 16²? =
26. 26.A square garden has an area of 400 square m. How long is each side (in m)?
27. 27.What is 52²? =
28. 28.A square garden has an area of 529 square m. How long is each side (in m)?
29. 29.How many whole numbers lie between 49² and 50²?
30. 30.What is the sum of the first 11 odd numbers (1 + 3 + 5 + …)?
31. 31.What is √7744? =
32. 32.What is 54²? =
33. 33.What is √1296? =
34. 34.What is 94²? =
35. 35.What is the smallest whole number by which 540 must be divided to get a perfect square?
36. 36.What is the smallest whole number by which 108 must be multiplied to get a perfect square?
37. 37.A square garden has an area of 2025 square m. How long is each side (in m)?
38. 38.What is 50²? =
39. 39.What is 28²? =
40. 40.A square garden has an area of 784 square m. How long is each side (in m)?

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