Class 8 Maths Worksheet: Squares and Square Roots

Maths worksheets lesson 58: Squares and square roots · Set 306 · 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 13²? =
2. 2.What is 77²? =
3. 3.What is 74²? =
4. 4.What is the sum of the first 28 odd numbers (1 + 3 + 5 + …)?
5. 5.How many whole numbers lie between 9² and 10²?
6. 6.What is the smallest whole number by which 896 must be multiplied to get a perfect square?
7. 7.What is 40²? =
8. 8.What is √1521? =
9. 9.A square garden has an area of 3025 square m. How long is each side (in m)?
10. 10.What is 18²? =
11. 11.How many whole numbers lie between 31² and 32²?
12. 12.What is the sum of the first 27 odd numbers (1 + 3 + 5 + …)?
13. 13.What is √169? =
14. 14.What is the smallest whole number by which 504 must be divided to get a perfect square?
15. 15.What is √8836? =
16. 16.Which of these is a perfect square? (a) 511 (b) 484 (c) 519
17. 17.How many whole numbers lie between 7² and 8²?
18. 18.What is √6400? =
19. 19.What is the sum of the first 13 odd numbers (1 + 3 + 5 + …)?
20. 20.What is the smallest whole number by which 135 must be multiplied to get a perfect square?
21. 21.What is √484? =
22. 22.What is √900? =
23. 23.How many whole numbers lie between 50² and 51²?
24. 24.What is the sum of the first 19 odd numbers (1 + 3 + 5 + …)?
25. 25.What is √6241? =
26. 26.What is 21²? =
27. 27.What is the smallest whole number by which 128 must be divided to get a perfect square?
28. 28.What is the smallest whole number by which 117 must be multiplied to get a perfect square?
29. 29.What is √9801? =
30. 30.A square garden has an area of 1600 square m. How long is each side (in m)?
31. 31.What is 22²? =
32. 32.What is the sum of the first 7 odd numbers (1 + 3 + 5 + …)?
33. 33.A square garden has an area of 25 square m. How long is each side (in m)?
34. 34.Which of these is a perfect square? (a) 1158 (b) 1197 (c) 1156
35. 35.A square garden has an area of 1681 square m. How long is each side (in m)?
36. 36.What is the smallest whole number by which 45 must be multiplied to get a perfect square?
37. 37.What is the sum of the first 6 odd numbers (1 + 3 + 5 + …)?
38. 38.What is the smallest whole number by which 486 must be multiplied to get a perfect square?
39. 39.A square garden has an area of 64 square m. How long is each side (in m)?
40. 40.What is the sum of the first 11 odd numbers (1 + 3 + 5 + …)?

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