Class 8 Maths Worksheet: Squares and Square Roots

Maths worksheets lesson 58: Squares and square roots · Set 326 · 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.How many whole numbers lie between 48² and 49²?
2. 2.What is 15²? =
3. 3.What is the smallest whole number by which 98 must be divided to get a perfect square?
4. 4.What is 69²? =
5. 5.What is the sum of the first 30 odd numbers (1 + 3 + 5 + …)?
6. 6.How many whole numbers lie between 35² and 36²?
7. 7.What is 91²? =
8. 8.What is 83²? =
9. 9.What is √441? =
10. 10.What is the sum of the first 21 odd numbers (1 + 3 + 5 + …)?
11. 11.What is √9409? =
12. 12.A square garden has an area of 529 square m. How long is each side (in m)?
13. 13.What is the sum of the first 20 odd numbers (1 + 3 + 5 + …)?
14. 14.What is √9025? =
15. 15.What is the smallest whole number by which 176 must be divided to get a perfect square?
16. 16.What is the sum of the first 15 odd numbers (1 + 3 + 5 + …)?
17. 17.What is the sum of the first 17 odd numbers (1 + 3 + 5 + …)?
18. 18.How many whole numbers lie between 18² and 19²?
19. 19.What is the sum of the first 5 odd numbers (1 + 3 + 5 + …)?
20. 20.A square garden has an area of 121 square m. How long is each side (in m)?
21. 21.What is √3364? =
22. 22.What is the sum of the first 9 odd numbers (1 + 3 + 5 + …)?
23. 23.What is 64²? =
24. 24.What is √1296? =
25. 25.What is the sum of the first 8 odd numbers (1 + 3 + 5 + …)?
26. 26.A square garden has an area of 81 square m. How long is each side (in m)?
27. 27.What is the smallest whole number by which 12 must be multiplied to get a perfect square?
28. 28.What is √1024? =
29. 29.What is the smallest whole number by which 50 must be multiplied to get a perfect square?
30. 30.What is 17²? =
31. 31.What is √2809? =
32. 32.How many whole numbers lie between 31² and 32²?
33. 33.What is √2500? =
34. 34.Which of these is a perfect square? (a) 332 (b) 341 (c) 324
35. 35.How many whole numbers lie between 29² and 30²?
36. 36.What is 40²? =
37. 37.What is the sum of the first 11 odd numbers (1 + 3 + 5 + …)?
38. 38.How many whole numbers lie between 19² and 20²?
39. 39.What is the smallest whole number by which 48 must be divided to get a perfect square?
40. 40.How many whole numbers lie between 9² and 10²?

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