Class 8 Maths Worksheet: Squares and Square Roots

Maths worksheets lesson 58: Squares and square roots · Set 375 · 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 8² and 9²?
2. 2.What is 20²? =
3. 3.Which of these is a perfect square? (a) 253 (b) 225 (c) 254
4. 4.What is 73²? =
5. 5.Which of these is a perfect square? (a) 256 (b) 260 (c) 258
6. 6.Which of these is a perfect square? (a) 1676 (b) 1636 (c) 1600
7. 7.What is 45²? =
8. 8.What is 91²? =
9. 9.What is 80²? =
10. 10.How many whole numbers lie between 37² and 38²?
11. 11.How many whole numbers lie between 49² and 50²?
12. 12.Which of these is a perfect square? (a) 1300 (b) 1296 (c) 1322
13. 13.A square garden has an area of 961 square m. How long is each side (in m)?
14. 14.What is the sum of the first 25 odd numbers (1 + 3 + 5 + …)?
15. 15.What is √7056? =
16. 16.What is the sum of the first 28 odd numbers (1 + 3 + 5 + …)?
17. 17.Which of these is a perfect square? (a) 174 (b) 189 (c) 169
18. 18.What is 17²? =
19. 19.What is the smallest whole number by which 63 must be divided to get a perfect square?
20. 20.What is the sum of the first 8 odd numbers (1 + 3 + 5 + …)?
21. 21.What is the smallest whole number by which 448 must be multiplied to get a perfect square?
22. 22.How many whole numbers lie between 36² and 37²?
23. 23.A square garden has an area of 1521 square m. How long is each side (in m)?
24. 24.What is 60²? =
25. 25.A square garden has an area of 2025 square m. How long is each side (in m)?
26. 26.Which of these is a perfect square? (a) 301 (b) 304 (c) 289
27. 27.What is 93²? =
28. 28.How many whole numbers lie between 40² and 41²?
29. 29.Which of these is a perfect square? (a) 114 (b) 100 (c) 120
30. 30.What is √2704? =
31. 31.What is √256? =
32. 32.Which of these is a perfect square? (a) 374 (b) 389 (c) 361
33. 33.What is the smallest whole number by which 396 must be divided to get a perfect square?
34. 34.What is √900? =
35. 35.What is √225? =
36. 36.How many whole numbers lie between 21² and 22²?
37. 37.What is the smallest whole number by which 63 must be multiplied to get a perfect square?
38. 38.What is the smallest whole number by which 250 must be multiplied to get a perfect square?
39. 39.What is 23²? =
40. 40.What is 94²? =

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