Class 8 Maths Worksheet: Squares and Square Roots

Maths worksheets lesson 58: Squares and square roots · Set 466 · 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.Which of these is a perfect square? (a) 303 (b) 289 (c) 302
2. 2.Which of these is a perfect square? (a) 529 (b) 531 (c) 572
3. 3.What is the smallest whole number by which 147 must be multiplied to get a perfect square?
4. 4.What is the sum of the first 10 odd numbers (1 + 3 + 5 + …)?
5. 5.A square garden has an area of 2809 square m. How long is each side (in m)?
6. 6.What is the sum of the first 11 odd numbers (1 + 3 + 5 + …)?
7. 7.A square garden has an area of 100 square m. How long is each side (in m)?
8. 8.A square garden has an area of 121 square m. How long is each side (in m)?
9. 9.What is 24²? =
10. 10.What is 47²? =
11. 11.What is the smallest whole number by which 240 must be divided to get a perfect square?
12. 12.What is the sum of the first 14 odd numbers (1 + 3 + 5 + …)?
13. 13.What is 43²? =
14. 14.What is √841? =
15. 15.What is the sum of the first 30 odd numbers (1 + 3 + 5 + …)?
16. 16.How many whole numbers lie between 14² and 15²?
17. 17.How many whole numbers lie between 38² and 39²?
18. 18.What is 22²? =
19. 19.What is 42²? =
20. 20.What is 72²? =
21. 21.What is the sum of the first 22 odd numbers (1 + 3 + 5 + …)?
22. 22.What is 25²? =
23. 23.Which of these is a perfect square? (a) 709 (b) 676 (c) 684
24. 24.What is the smallest whole number by which 48 must be multiplied to get a perfect square?
25. 25.A square garden has an area of 144 square m. How long is each side (in m)?
26. 26.A square garden has an area of 36 square m. How long is each side (in m)?
27. 27.How many whole numbers lie between 47² and 48²?
28. 28.A square garden has an area of 1225 square m. How long is each side (in m)?
29. 29.How many whole numbers lie between 39² and 40²?
30. 30.What is √1225? =
31. 31.Which of these is a perfect square? (a) 668 (b) 625 (c) 642
32. 32.What is √5476? =
33. 33.What is the smallest whole number by which 375 must be divided to get a perfect square?
34. 34.What is 86²? =
35. 35.What is √256? =
36. 36.A square garden has an area of 2601 square m. How long is each side (in m)?
37. 37.Which of these is a perfect square? (a) 225 (b) 239 (c) 242
38. 38.Which of these is a perfect square? (a) 109 (b) 101 (c) 100
39. 39.A square garden has an area of 1764 square m. How long is each side (in m)?
40. 40.What is 73²? =

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