Class 8 Maths Worksheet: Squares and Square Roots

Maths worksheets lesson 58: Squares and square roots · Set 493 · 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 40 must be divided to get a perfect square?
2. 2.What is the sum of the first 8 odd numbers (1 + 3 + 5 + …)?
3. 3.How many whole numbers lie between 48² and 49²?
4. 4.What is √1444? =
5. 5.What is √6724? =
6. 6.How many whole numbers lie between 13² and 14²?
7. 7.What is √2704? =
8. 8.What is the smallest whole number by which 704 must be multiplied to get a perfect square?
9. 9.A square garden has an area of 3364 square m. How long is each side (in m)?
10. 10.What is 27²? =
11. 11.What is 12²? =
12. 12.Which of these is a perfect square? (a) 1600 (b) 1618 (c) 1648
13. 13.What is the sum of the first 9 odd numbers (1 + 3 + 5 + …)?
14. 14.Which of these is a perfect square? (a) 120 (b) 107 (c) 100
15. 15.What is √5476? =
16. 16.What is √1156? =
17. 17.What is 61²? =
18. 18.What is the sum of the first 29 odd numbers (1 + 3 + 5 + …)?
19. 19.Which of these is a perfect square? (a) 443 (b) 454 (c) 441
20. 20.What is √1936? =
21. 21.What is 93²? =
22. 22.How many whole numbers lie between 49² and 50²?
23. 23.A square garden has an area of 441 square m. How long is each side (in m)?
24. 24.Which of these is a perfect square? (a) 192 (b) 185 (c) 169
25. 25.How many whole numbers lie between 12² and 13²?
26. 26.What is 95²? =
27. 27.What is 47²? =
28. 28.What is √1764? =
29. 29.How many whole numbers lie between 20² and 21²?
30. 30.How many whole numbers lie between 41² and 42²?
31. 31.What is 51²? =
32. 32.How many whole numbers lie between 37² and 38²?
33. 33.What is the smallest whole number by which 245 must be divided to get a perfect square?
34. 34.What is the smallest whole number by which 686 must be divided to get a perfect square?
35. 35.What is the sum of the first 23 odd numbers (1 + 3 + 5 + …)?
36. 36.A square garden has an area of 2304 square m. How long is each side (in m)?
37. 37.What is the smallest whole number by which 45 must be multiplied to get a perfect square?
38. 38.Which of these is a perfect square? (a) 144 (b) 156 (c) 145
39. 39.Which of these is a perfect square? (a) 386 (b) 361 (c) 381
40. 40.What is √900? =

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