Class 8 Maths Worksheet: Squares and Square Roots

Maths worksheets lesson 58: Squares and square roots · Set 437 · 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.A square garden has an area of 361 square m. How long is each side (in m)?
2. 2.What is 70²? =
3. 3.What is the smallest whole number by which 294 must be multiplied to get a perfect square?
4. 4.What is the sum of the first 28 odd numbers (1 + 3 + 5 + …)?
5. 5.What is √289? =
6. 6.What is 72²? =
7. 7.What is the smallest whole number by which 48 must be divided to get a perfect square?
8. 8.What is 38²? =
9. 9.What is 80²? =
10. 10.What is 18²? =
11. 11.What is √5184? =
12. 12.What is 48²? =
13. 13.A square garden has an area of 3136 square m. How long is each side (in m)?
14. 14.What is 42²? =
15. 15.What is √576? =
16. 16.What is 33²? =
17. 17.What is 83²? =
18. 18.What is 86²? =
19. 19.Which of these is a perfect square? (a) 971 (b) 1004 (c) 961
20. 20.A square garden has an area of 1764 square m. How long is each side (in m)?
21. 21.How many whole numbers lie between 23² and 24²?
22. 22.What is 67²? =
23. 23.What is √3249? =
24. 24.What is 46²? =
25. 25.What is the smallest whole number by which 56 must be divided to get a perfect square?
26. 26.Which of these is a perfect square? (a) 581 (b) 620 (c) 576
27. 27.What is the smallest whole number by which 162 must be multiplied to get a perfect square?
28. 28.What is √2209? =
29. 29.What is √9409? =
30. 30.What is √8281? =
31. 31.What is the smallest whole number by which 960 must be divided to get a perfect square?
32. 32.Which of these is a perfect square? (a) 1353 (b) 1296 (c) 1328
33. 33.Which of these is a perfect square? (a) 418 (b) 434 (c) 400
34. 34.What is the sum of the first 6 odd numbers (1 + 3 + 5 + …)?
35. 35.What is √3364? =
36. 36.What is the smallest whole number by which 72 must be multiplied to get a perfect square?
37. 37.What is 15²? =
38. 38.What is the smallest whole number by which 128 must be multiplied to get a perfect square?
39. 39.How many whole numbers lie between 35² and 36²?
40. 40.What is √6561? =

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