Class 8 Maths Worksheet: Squares and Square Roots

Maths worksheets lesson 58: Squares and square roots · Set 229 · 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.How many whole numbers lie between 38² and 39²?
2. 2.A square garden has an area of 576 square m. How long is each side (in m)?
3. 3.What is 60²? =
4. 4.Which of these is a perfect square? (a) 1376 (b) 1424 (c) 1369
5. 5.Which of these is a perfect square? (a) 207 (b) 196 (c) 217
6. 6.What is the sum of the first 14 odd numbers (1 + 3 + 5 + …)?
7. 7.What is 26²? =
8. 8.What is 71²? =
9. 9.What is the sum of the first 10 odd numbers (1 + 3 + 5 + …)?
10. 10.What is the sum of the first 19 odd numbers (1 + 3 + 5 + …)?
11. 11.What is √8649? =
12. 12.What is 32²? =
13. 13.What is √4356? =
14. 14.How many whole numbers lie between 29² and 30²?
15. 15.How many whole numbers lie between 43² and 44²?
16. 16.What is 35²? =
17. 17.What is 55²? =
18. 18.What is the sum of the first 21 odd numbers (1 + 3 + 5 + …)?
19. 19.What is 78²? =
20. 20.What is √1369? =
21. 21.How many whole numbers lie between 34² and 35²?
22. 22.What is the sum of the first 12 odd numbers (1 + 3 + 5 + …)?
23. 23.How many whole numbers lie between 6² and 7²?
24. 24.What is 98²? =
25. 25.Which of these is a perfect square? (a) 1521 (b) 1595 (c) 1535
26. 26.A square garden has an area of 1225 square m. How long is each side (in m)?
27. 27.A square garden has an area of 529 square m. How long is each side (in m)?
28. 28.What is the smallest whole number by which 12 must be divided to get a perfect square?
29. 29.What is √9409? =
30. 30.What is 49²? =
31. 31.What is the smallest whole number by which 56 must be multiplied to get a perfect square?
32. 32.What is 38²? =
33. 33.What is the smallest whole number by which 44 must be divided to get a perfect square?
34. 34.What is 43²? =
35. 35.What is the sum of the first 24 odd numbers (1 + 3 + 5 + …)?
36. 36.What is the smallest whole number by which 567 must be multiplied to get a perfect square?
37. 37.What is the smallest whole number by which 686 must be divided to get a perfect square?
38. 38.What is √784? =
39. 39.How many whole numbers lie between 30² and 31²?
40. 40.A square garden has an area of 2704 square m. How long is each side (in m)?

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