Class 8 Maths Worksheet: Squares and Square Roots

Maths worksheets lesson 58: Squares and square roots · Set 710 · 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 81²? =
2. 2.What is the sum of the first 15 odd numbers (1 + 3 + 5 + …)?
3. 3.What is 18²? =
4. 4.A square garden has an area of 529 square m. How long is each side (in m)?
5. 5.What is 31²? =
6. 6.A square garden has an area of 2601 square m. How long is each side (in m)?
7. 7.What is the sum of the first 10 odd numbers (1 + 3 + 5 + …)?
8. 8.What is 59²? =
9. 9.What is 54²? =
10. 10.A square garden has an area of 1024 square m. How long is each side (in m)?
11. 11.What is 35²? =
12. 12.What is 88²? =
13. 13.What is 38²? =
14. 14.What is √1936? =
15. 15.Which of these is a perfect square? (a) 463 (b) 441 (c) 443
16. 16.What is √6889? =
17. 17.Which of these is a perfect square? (a) 145 (b) 144 (c) 158
18. 18.What is the smallest whole number by which 54 must be divided to get a perfect square?
19. 19.What is the sum of the first 14 odd numbers (1 + 3 + 5 + …)?
20. 20.What is the sum of the first 29 odd numbers (1 + 3 + 5 + …)?
21. 21.What is √8464? =
22. 22.Which of these is a perfect square? (a) 196 (b) 220 (c) 198
23. 23.A square garden has an area of 2116 square m. How long is each side (in m)?
24. 24.What is 43²? =
25. 25.What is the smallest whole number by which 294 must be multiplied to get a perfect square?
26. 26.How many whole numbers lie between 20² and 21²?
27. 27.What is the smallest whole number by which 243 must be multiplied to get a perfect square?
28. 28.What is √2601? =
29. 29.Which of these is a perfect square? (a) 120 (b) 107 (c) 100
30. 30.A square garden has an area of 169 square m. How long is each side (in m)?
31. 31.How many whole numbers lie between 21² and 22²?
32. 32.How many whole numbers lie between 35² and 36²?
33. 33.What is √5776? =
34. 34.What is √9409? =
35. 35.What is the smallest whole number by which 63 must be multiplied to get a perfect square?
36. 36.What is the sum of the first 12 odd numbers (1 + 3 + 5 + …)?
37. 37.What is √2209? =
38. 38.What is the smallest whole number by which 24 must be divided to get a perfect square?
39. 39.What is √1600? =
40. 40.What is the sum of the first 23 odd numbers (1 + 3 + 5 + …)?

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