Class 8 Maths Worksheet: Squares and Square Roots

Maths worksheets lesson 58: Squares and square roots · Set 633 · 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 the sum of the first 10 odd numbers (1 + 3 + 5 + …)?
2. 2.What is 82²? =
3. 3.What is the sum of the first 20 odd numbers (1 + 3 + 5 + …)?
4. 4.What is 97²? =
5. 5.What is √5041? =
6. 6.A square garden has an area of 1521 square m. How long is each side (in m)?
7. 7.What is the sum of the first 17 odd numbers (1 + 3 + 5 + …)?
8. 8.What is 76²? =
9. 9.What is 60²? =
10. 10.A square garden has an area of 49 square m. How long is each side (in m)?
11. 11.What is 70²? =
12. 12.A square garden has an area of 3136 square m. How long is each side (in m)?
13. 13.What is 43²? =
14. 14.What is √1024? =
15. 15.How many whole numbers lie between 29² and 30²?
16. 16.How many whole numbers lie between 12² and 13²?
17. 17.What is the smallest whole number by which 162 must be divided to get a perfect square?
18. 18.A square garden has an area of 400 square m. How long is each side (in m)?
19. 19.What is 67²? =
20. 20.What is the sum of the first 26 odd numbers (1 + 3 + 5 + …)?
21. 21.What is the smallest whole number by which 28 must be multiplied to get a perfect square?
22. 22.What is √2809? =
23. 23.What is √169? =
24. 24.What is √6724? =
25. 25.What is 87²? =
26. 26.Which of these is a perfect square? (a) 374 (b) 361 (c) 372
27. 27.What is the smallest whole number by which 50 must be multiplied to get a perfect square?
28. 28.What is 69²? =
29. 29.What is 32²? =
30. 30.Which of these is a perfect square? (a) 170 (b) 176 (c) 169
31. 31.What is 22²? =
32. 32.A square garden has an area of 225 square m. How long is each side (in m)?
33. 33.What is 36²? =
34. 34.What is 23²? =
35. 35.How many whole numbers lie between 33² and 34²?
36. 36.Which of these is a perfect square? (a) 1085 (b) 1038 (c) 1024
37. 37.A square garden has an area of 2809 square m. How long is each side (in m)?
38. 38.How many whole numbers lie between 6² and 7²?
39. 39.What is 45²? =
40. 40.How many whole numbers lie between 18² and 19²?

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