Class 8 Maths Worksheet: Squares and Square Roots

Maths worksheets lesson 58: Squares and square roots · Set 586 · 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 the sum of the first 28 odd numbers (1 + 3 + 5 + …)?
2. 2.Which of these is a perfect square? (a) 834 (b) 784 (c) 788
3. 3.What is √9604? =
4. 4.What is the sum of the first 5 odd numbers (1 + 3 + 5 + …)?
5. 5.What is the smallest whole number by which 735 must be multiplied to get a perfect square?
6. 6.What is the smallest whole number by which 99 must be multiplied to get a perfect square?
7. 7.What is 49²? =
8. 8.What is the sum of the first 8 odd numbers (1 + 3 + 5 + …)?
9. 9.What is the sum of the first 25 odd numbers (1 + 3 + 5 + …)?
10. 10.What is 71²? =
11. 11.A square garden has an area of 49 square m. How long is each side (in m)?
12. 12.What is 34²? =
13. 13.What is 38²? =
14. 14.How many whole numbers lie between 15² and 16²?
15. 15.Which of these is a perfect square? (a) 556 (b) 563 (c) 529
16. 16.What is √3249? =
17. 17.A square garden has an area of 1600 square m. How long is each side (in m)?
18. 18.How many whole numbers lie between 43² and 44²?
19. 19.Which of these is a perfect square? (a) 359 (b) 326 (c) 324
20. 20.What is the smallest whole number by which 448 must be divided to get a perfect square?
21. 21.What is the smallest whole number by which 90 must be divided to get a perfect square?
22. 22.What is 95²? =
23. 23.How many whole numbers lie between 11² and 12²?
24. 24.What is 97²? =
25. 25.How many whole numbers lie between 28² and 29²?
26. 26.What is 84²? =
27. 27.What is 80²? =
28. 28.What is 11²? =
29. 29.How many whole numbers lie between 35² and 36²?
30. 30.Which of these is a perfect square? (a) 642 (b) 625 (c) 646
31. 31.What is the sum of the first 19 odd numbers (1 + 3 + 5 + …)?
32. 32.What is 70²? =
33. 33.What is the sum of the first 11 odd numbers (1 + 3 + 5 + …)?
34. 34.What is the smallest whole number by which 810 must be divided to get a perfect square?
35. 35.What is the smallest whole number by which 192 must be multiplied to get a perfect square?
36. 36.What is the smallest whole number by which 325 must be multiplied to get a perfect square?
37. 37.What is the sum of the first 17 odd numbers (1 + 3 + 5 + …)?
38. 38.What is 81²? =
39. 39.What is the smallest whole number by which 540 must be multiplied to get a perfect square?
40. 40.What is the smallest whole number by which 99 must be divided to get a perfect square?

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