Class 8 Maths Worksheet: Squares and Square Roots

Maths worksheets lesson 58: Squares and square roots · Set 45 · 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.What is 96²? =
2. 2.What is the sum of the first 19 odd numbers (1 + 3 + 5 + …)?
3. 3.Which of these is a perfect square? (a) 948 (b) 953 (c) 900
4. 4.What is √676? =
5. 5.How many whole numbers lie between 15² and 16²?
6. 6.What is the smallest whole number by which 162 must be multiplied to get a perfect square?
7. 7.What is the sum of the first 21 odd numbers (1 + 3 + 5 + …)?
8. 8.What is the smallest whole number by which 891 must be divided to get a perfect square?
9. 9.What is the smallest whole number by which 350 must be divided to get a perfect square?
10. 10.How many whole numbers lie between 19² and 20²?
11. 11.What is 62²? =
12. 12.What is √2916? =
13. 13.What is the smallest whole number by which 45 must be multiplied to get a perfect square?
14. 14.What is √8649? =
15. 15.Which of these is a perfect square? (a) 361 (b) 367 (c) 376
16. 16.What is 28²? =
17. 17.A square garden has an area of 3600 square m. How long is each side (in m)?
18. 18.Which of these is a perfect square? (a) 204 (b) 196 (c) 221
19. 19.What is 42²? =
20. 20.What is the sum of the first 28 odd numbers (1 + 3 + 5 + …)?
21. 21.Which of these is a perfect square? (a) 1299 (b) 1296 (c) 1307
22. 22.What is √3600? =
23. 23.How many whole numbers lie between 38² and 39²?
24. 24.Which of these is a perfect square? (a) 1369 (b) 1385 (c) 1391
25. 25.What is √225? =
26. 26.A square garden has an area of 196 square m. How long is each side (in m)?
27. 27.What is 98²? =
28. 28.A square garden has an area of 64 square m. How long is each side (in m)?
29. 29.What is the smallest whole number by which 343 must be multiplied to get a perfect square?
30. 30.What is 48²? =
31. 31.How many whole numbers lie between 17² and 18²?
32. 32.A square garden has an area of 1936 square m. How long is each side (in m)?
33. 33.How many whole numbers lie between 34² and 35²?
34. 34.What is 80²? =
35. 35.Which of these is a perfect square? (a) 1030 (b) 1051 (c) 1024
36. 36.Which of these is a perfect square? (a) 133 (b) 129 (c) 121
37. 37.What is √6724? =
38. 38.What is the sum of the first 17 odd numbers (1 + 3 + 5 + …)?
39. 39.Which of these is a perfect square? (a) 655 (b) 625 (c) 650
40. 40.What is the smallest whole number by which 135 must be divided to get a perfect square?

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