Class 8 Maths Worksheet: Squares and Square Roots

Maths worksheets lesson 58: Squares and square roots · Set 139 · 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 5 odd numbers (1 + 3 + 5 + …)?
2. 2.What is the sum of the first 27 odd numbers (1 + 3 + 5 + …)?
3. 3.What is the smallest whole number by which 99 must be divided to get a perfect square?
4. 4.What is 38²? =
5. 5.Which of these is a perfect square? (a) 447 (b) 473 (c) 441
6. 6.What is 41²? =
7. 7.How many whole numbers lie between 46² and 47²?
8. 8.What is √3249? =
9. 9.Which of these is a perfect square? (a) 1046 (b) 1024 (c) 1035
10. 10.Which of these is a perfect square? (a) 1139 (b) 1089 (c) 1116
11. 11.A square garden has an area of 25 square m. How long is each side (in m)?
12. 12.A square garden has an area of 144 square m. How long is each side (in m)?
13. 13.What is the smallest whole number by which 12 must be multiplied to get a perfect square?
14. 14.A square garden has an area of 1600 square m. How long is each side (in m)?
15. 15.What is 11²? =
16. 16.What is the smallest whole number by which 405 must be multiplied to get a perfect square?
17. 17.What is √3364? =
18. 18.What is the smallest whole number by which 468 must be multiplied to get a perfect square?
19. 19.What is the sum of the first 20 odd numbers (1 + 3 + 5 + …)?
20. 20.What is √256? =
21. 21.A square garden has an area of 289 square m. How long is each side (in m)?
22. 22.What is 90²? =
23. 23.Which of these is a perfect square? (a) 347 (b) 353 (c) 324
24. 24.What is 13²? =
25. 25.What is the sum of the first 22 odd numbers (1 + 3 + 5 + …)?
26. 26.A square garden has an area of 2601 square m. How long is each side (in m)?
27. 27.A square garden has an area of 361 square m. How long is each side (in m)?
28. 28.What is √6084? =
29. 29.What is 82²? =
30. 30.What is 93²? =
31. 31.How many whole numbers lie between 33² and 34²?
32. 32.What is the sum of the first 15 odd numbers (1 + 3 + 5 + …)?
33. 33.What is the sum of the first 26 odd numbers (1 + 3 + 5 + …)?
34. 34.How many whole numbers lie between 15² and 16²?
35. 35.How many whole numbers lie between 7² and 8²?
36. 36.What is the smallest whole number by which 960 must be multiplied to get a perfect square?
37. 37.What is √5776? =
38. 38.Which of these is a perfect square? (a) 196 (b) 205 (c) 199
39. 39.What is √121? =
40. 40.What is the smallest whole number by which 245 must be multiplied to get a perfect square?

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