Class 8 Maths Worksheet: Squares and Square Roots

Maths worksheets lesson 58: Squares and square roots · Set 18 · 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 smallest whole number by which 56 must be multiplied to get a perfect square?
2. 2.What is 68²? =
3. 3.What is 46²? =
4. 4.What is the sum of the first 26 odd numbers (1 + 3 + 5 + …)?
5. 5.What is the sum of the first 18 odd numbers (1 + 3 + 5 + …)?
6. 6.What is 19²? =
7. 7.What is the smallest whole number by which 98 must be divided to get a perfect square?
8. 8.What is 33²? =
9. 9.What is 30²? =
10. 10.How many whole numbers lie between 8² and 9²?
11. 11.Which of these is a perfect square? (a) 361 (b) 389 (c) 381
12. 12.What is the sum of the first 24 odd numbers (1 + 3 + 5 + …)?
13. 13.How many whole numbers lie between 40² and 41²?
14. 14.What is the smallest whole number by which 192 must be multiplied to get a perfect square?
15. 15.What is the smallest whole number by which 50 must be multiplied to get a perfect square?
16. 16.What is √2500? =
17. 17.What is √324? =
18. 18.What is 50²? =
19. 19.What is √2025? =
20. 20.What is the sum of the first 23 odd numbers (1 + 3 + 5 + …)?
21. 21.What is 78²? =
22. 22.What is 41²? =
23. 23.What is √3600? =
24. 24.What is the smallest whole number by which 44 must be divided to get a perfect square?
25. 25.How many whole numbers lie between 20² and 21²?
26. 26.What is √5625? =
27. 27.What is √3025? =
28. 28.A square garden has an area of 784 square m. How long is each side (in m)?
29. 29.What is √676? =
30. 30.What is 38²? =
31. 31.Which of these is a perfect square? (a) 1669 (b) 1651 (c) 1600
32. 32.What is √4900? =
33. 33.How many whole numbers lie between 30² and 31²?
34. 34.Which of these is a perfect square? (a) 314 (b) 321 (c) 289
35. 35.What is the sum of the first 10 odd numbers (1 + 3 + 5 + …)?
36. 36.Which of these is a perfect square? (a) 484 (b) 488 (c) 521
37. 37.A square garden has an area of 144 square m. How long is each side (in m)?
38. 38.What is 90²? =
39. 39.How many whole numbers lie between 27² and 28²?
40. 40.A square garden has an area of 361 square m. How long is each side (in m)?

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