Class 8 Maths Worksheet: Squares and Square Roots

Maths worksheets lesson 58: Squares and square roots · Set 384 · 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 48²? =
2. 2.How many whole numbers lie between 8² and 9²?
3. 3.What is 36²? =
4. 4.How many whole numbers lie between 11² and 12²?
5. 5.What is the smallest whole number by which 1134 must be divided to get a perfect square?
6. 6.What is the sum of the first 30 odd numbers (1 + 3 + 5 + …)?
7. 7.What is the sum of the first 7 odd numbers (1 + 3 + 5 + …)?
8. 8.What is 18²? =
9. 9.How many whole numbers lie between 6² and 7²?
10. 10.What is √144? =
11. 11.How many whole numbers lie between 28² and 29²?
12. 12.What is the sum of the first 18 odd numbers (1 + 3 + 5 + …)?
13. 13.What is √625? =
14. 14.What is the sum of the first 15 odd numbers (1 + 3 + 5 + …)?
15. 15.Which of these is a perfect square? (a) 1168 (b) 1156 (c) 1163
16. 16.What is 56²? =
17. 17.Which of these is a perfect square? (a) 1039 (b) 1024 (c) 1040
18. 18.What is √2500? =
19. 19.What is the smallest whole number by which 162 must be multiplied to get a perfect square?
20. 20.What is the smallest whole number by which 360 must be multiplied to get a perfect square?
21. 21.Which of these is a perfect square? (a) 1369 (b) 1425 (c) 1396
22. 22.What is 33²? =
23. 23.What is 85²? =
24. 24.A square garden has an area of 3364 square m. How long is each side (in m)?
25. 25.How many whole numbers lie between 42² and 43²?
26. 26.What is the sum of the first 16 odd numbers (1 + 3 + 5 + …)?
27. 27.What is 40²? =
28. 28.What is the sum of the first 14 odd numbers (1 + 3 + 5 + …)?
29. 29.How many whole numbers lie between 32² and 33²?
30. 30.What is 16²? =
31. 31.A square garden has an area of 3249 square m. How long is each side (in m)?
32. 32.What is 60²? =
33. 33.What is the sum of the first 22 odd numbers (1 + 3 + 5 + …)?
34. 34.What is the smallest whole number by which 192 must be divided to get a perfect square?
35. 35.What is the sum of the first 17 odd numbers (1 + 3 + 5 + …)?
36. 36.A square garden has an area of 256 square m. How long is each side (in m)?
37. 37.What is 82²? =
38. 38.What is √6400? =
39. 39.A square garden has an area of 2809 square m. How long is each side (in m)?
40. 40.What is the sum of the first 26 odd numbers (1 + 3 + 5 + …)?

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