Class 8 Maths Worksheet: Squares and Square Roots

Maths worksheets lesson 58: Squares and square roots · Set 34 · 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.A square garden has an area of 529 square m. How long is each side (in m)?
2. 2.A square garden has an area of 25 square m. How long is each side (in m)?
3. 3.What is the sum of the first 10 odd numbers (1 + 3 + 5 + …)?
4. 4.What is 19²? =
5. 5.What is √900? =
6. 6.What is 49²? =
7. 7.What is the sum of the first 6 odd numbers (1 + 3 + 5 + …)?
8. 8.What is √9409? =
9. 9.Which of these is a perfect square? (a) 1177 (b) 1156 (c) 1206
10. 10.What is the sum of the first 11 odd numbers (1 + 3 + 5 + …)?
11. 11.What is the sum of the first 8 odd numbers (1 + 3 + 5 + …)?
12. 12.What is 67²? =
13. 13.What is the sum of the first 7 odd numbers (1 + 3 + 5 + …)?
14. 14.What is the sum of the first 30 odd numbers (1 + 3 + 5 + …)?
15. 15.How many whole numbers lie between 38² and 39²?
16. 16.What is the smallest whole number by which 126 must be divided to get a perfect square?
17. 17.How many whole numbers lie between 34² and 35²?
18. 18.What is the sum of the first 27 odd numbers (1 + 3 + 5 + …)?
19. 19.What is 44²? =
20. 20.What is the smallest whole number by which 832 must be multiplied to get a perfect square?
21. 21.Which of these is a perfect square? (a) 412 (b) 429 (c) 400
22. 22.What is 53²? =
23. 23.Which of these is a perfect square? (a) 1649 (b) 1670 (c) 1600
24. 24.What is √4900? =
25. 25.How many whole numbers lie between 12² and 13²?
26. 26.What is √3600? =
27. 27.What is 94²? =
28. 28.How many whole numbers lie between 45² and 46²?
29. 29.What is the smallest whole number by which 50 must be divided to get a perfect square?
30. 30.Which of these is a perfect square? (a) 110 (b) 109 (c) 100
31. 31.How many whole numbers lie between 32² and 33²?
32. 32.How many whole numbers lie between 10² and 11²?
33. 33.What is √9801? =
34. 34.What is 57²? =
35. 35.What is the smallest whole number by which 208 must be divided to get a perfect square?
36. 36.What is 27²? =
37. 37.What is the sum of the first 17 odd numbers (1 + 3 + 5 + …)?
38. 38.What is the sum of the first 25 odd numbers (1 + 3 + 5 + …)?
39. 39.Which of these is a perfect square? (a) 935 (b) 949 (c) 900
40. 40.What is the sum of the first 26 odd numbers (1 + 3 + 5 + …)?

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