Class 8 Maths Worksheet: Squares and Square Roots

Maths worksheets lesson 58: Squares and square roots · Set 392 · 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 √8649? =
2. 2.What is the smallest whole number by which 28 must be multiplied to get a perfect square?
3. 3.What is the sum of the first 19 odd numbers (1 + 3 + 5 + …)?
4. 4.What is 44²? =
5. 5.What is √400? =
6. 6.What is 13²? =
7. 7.Which of these is a perfect square? (a) 900 (b) 952 (c) 908
8. 8.What is the smallest whole number by which 48 must be multiplied to get a perfect square?
9. 9.What is 45²? =
10. 10.How many whole numbers lie between 49² and 50²?
11. 11.What is the sum of the first 26 odd numbers (1 + 3 + 5 + …)?
12. 12.What is the sum of the first 12 odd numbers (1 + 3 + 5 + …)?
13. 13.What is the smallest whole number by which 80 must be multiplied to get a perfect square?
14. 14.How many whole numbers lie between 18² and 19²?
15. 15.What is the smallest whole number by which 343 must be divided to get a perfect square?
16. 16.Which of these is a perfect square? (a) 100 (b) 109 (c) 108
17. 17.What is 48²? =
18. 18.A square garden has an area of 3025 square m. How long is each side (in m)?
19. 19.What is the smallest whole number by which 245 must be multiplied to get a perfect square?
20. 20.A square garden has an area of 900 square m. How long is each side (in m)?
21. 21.What is √121? =
22. 22.What is 55²? =
23. 23.What is the smallest whole number by which 325 must be divided to get a perfect square?
24. 24.A square garden has an area of 36 square m. How long is each side (in m)?
25. 25.What is √3364? =
26. 26.How many whole numbers lie between 12² and 13²?
27. 27.Which of these is a perfect square? (a) 529 (b) 532 (c) 558
28. 28.What is 53²? =
29. 29.How many whole numbers lie between 15² and 16²?
30. 30.What is the sum of the first 6 odd numbers (1 + 3 + 5 + …)?
31. 31.What is 15²? =
32. 32.What is √2209? =
33. 33.A square garden has an area of 169 square m. How long is each side (in m)?
34. 34.What is the smallest whole number by which 240 must be divided to get a perfect square?
35. 35.What is √324? =
36. 36.Which of these is a perfect square? (a) 478 (b) 441 (c) 447
37. 37.A square garden has an area of 64 square m. How long is each side (in m)?
38. 38.What is 97²? =
39. 39.How many whole numbers lie between 19² and 20²?
40. 40.What is 93²? =

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