Class 8 Maths Worksheet: Squares and Square Roots

Maths worksheets lesson 58: Squares and square roots · Set 386 · 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 √484? =
2. 2.What is 15²? =
3. 3.What is the smallest whole number by which 32 must be multiplied to get a perfect square?
4. 4.What is 45²? =
5. 5.What is the smallest whole number by which 96 must be multiplied to get a perfect square?
6. 6.Which of these is a perfect square? (a) 337 (b) 344 (c) 324
7. 7.What is √2025? =
8. 8.What is the smallest whole number by which 128 must be multiplied to get a perfect square?
9. 9.What is the smallest whole number by which 686 must be divided to get a perfect square?
10. 10.A square garden has an area of 3600 square m. How long is each side (in m)?
11. 11.What is 14²? =
12. 12.What is the sum of the first 8 odd numbers (1 + 3 + 5 + …)?
13. 13.A square garden has an area of 529 square m. How long is each side (in m)?
14. 14.Which of these is a perfect square? (a) 107 (b) 100 (c) 118
15. 15.What is the sum of the first 29 odd numbers (1 + 3 + 5 + …)?
16. 16.What is √289? =
17. 17.A square garden has an area of 25 square m. How long is each side (in m)?
18. 18.What is the smallest whole number by which 99 must be divided to get a perfect square?
19. 19.Which of these is a perfect square? (a) 841 (b) 848 (c) 889
20. 20.What is √9409? =
21. 21.Which of these is a perfect square? (a) 182 (b) 169 (c) 184
22. 22.What is √169? =
23. 23.What is 66²? =
24. 24.What is the smallest whole number by which 12 must be divided to get a perfect square?
25. 25.A square garden has an area of 1296 square m. How long is each side (in m)?
26. 26.What is 46²? =
27. 27.What is √1849? =
28. 28.What is 71²? =
29. 29.How many whole numbers lie between 24² and 25²?
30. 30.What is the smallest whole number by which 810 must be multiplied to get a perfect square?
31. 31.What is 56²? =
32. 32.How many whole numbers lie between 50² and 51²?
33. 33.What is the sum of the first 12 odd numbers (1 + 3 + 5 + …)?
34. 34.A square garden has an area of 1681 square m. How long is each side (in m)?
35. 35.What is 72²? =
36. 36.What is 42²? =
37. 37.What is √5476? =
38. 38.Which of these is a perfect square? (a) 290 (b) 289 (c) 298
39. 39.How many whole numbers lie between 33² and 34²?
40. 40.How many whole numbers lie between 6² and 7²?

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