Class 8 Maths Worksheet: Squares and Square Roots

Maths worksheets lesson 58: Squares and square roots · Set 230 · 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 5² and 6²?
2. 2.How many whole numbers lie between 14² and 15²?
3. 3.What is √9604? =
4. 4.How many whole numbers lie between 31² and 32²?
5. 5.What is 36²? =
6. 6.What is the smallest whole number by which 72 must be multiplied to get a perfect square?
7. 7.What is the sum of the first 20 odd numbers (1 + 3 + 5 + …)?
8. 8.What is √1936? =
9. 9.What is the smallest whole number by which 60 must be multiplied to get a perfect square?
10. 10.What is the sum of the first 16 odd numbers (1 + 3 + 5 + …)?
11. 11.What is √2601? =
12. 12.What is the sum of the first 26 odd numbers (1 + 3 + 5 + …)?
13. 13.What is √6400? =
14. 14.What is the smallest whole number by which 50 must be divided to get a perfect square?
15. 15.What is the sum of the first 29 odd numbers (1 + 3 + 5 + …)?
16. 16.What is √1849? =
17. 17.What is 20²? =
18. 18.Which of these is a perfect square? (a) 107 (b) 100 (c) 103
19. 19.What is 45²? =
20. 20.A square garden has an area of 1936 square m. How long is each side (in m)?
21. 21.Which of these is a perfect square? (a) 1329 (b) 1296 (c) 1324
22. 22.What is the smallest whole number by which 468 must be divided to get a perfect square?
23. 23.What is √784? =
24. 24.What is the sum of the first 25 odd numbers (1 + 3 + 5 + …)?
25. 25.What is √4761? =
26. 26.What is √625? =
27. 27.What is the smallest whole number by which 28 must be multiplied to get a perfect square?
28. 28.What is 13²? =
29. 29.Which of these is a perfect square? (a) 1565 (b) 1521 (c) 1562
30. 30.A square garden has an area of 144 square m. How long is each side (in m)?
31. 31.What is the sum of the first 7 odd numbers (1 + 3 + 5 + …)?
32. 32.Which of these is a perfect square? (a) 1172 (b) 1161 (c) 1156
33. 33.What is the sum of the first 13 odd numbers (1 + 3 + 5 + …)?
34. 34.What is √2916? =
35. 35.How many whole numbers lie between 44² and 45²?
36. 36.A square garden has an area of 361 square m. How long is each side (in m)?
37. 37.What is the sum of the first 12 odd numbers (1 + 3 + 5 + …)?
38. 38.What is √6241? =
39. 39.What is the smallest whole number by which 108 must be divided to get a perfect square?
40. 40.What is the smallest whole number by which 175 must be multiplied to get a perfect square?

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