Class 8 Maths Worksheet: Squares and Square Roots

Maths worksheets lesson 58: Squares and square roots · Set 222 · 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 50²? =
2. 2.A square garden has an area of 2601 square m. How long is each side (in m)?
3. 3.What is the smallest whole number by which 8 must be divided to get a perfect square?
4. 4.A square garden has an area of 576 square m. How long is each side (in m)?
5. 5.How many whole numbers lie between 39² and 40²?
6. 6.What is the smallest whole number by which 375 must be multiplied to get a perfect square?
7. 7.What is 88²? =
8. 8.A square garden has an area of 2304 square m. How long is each side (in m)?
9. 9.What is the sum of the first 18 odd numbers (1 + 3 + 5 + …)?
10. 10.What is 25²? =
11. 11.A square garden has an area of 2209 square m. How long is each side (in m)?
12. 12.A square garden has an area of 1369 square m. How long is each side (in m)?
13. 13.What is the sum of the first 17 odd numbers (1 + 3 + 5 + …)?
14. 14.What is √7396? =
15. 15.Which of these is a perfect square? (a) 716 (b) 679 (c) 676
16. 16.What is the smallest whole number by which 891 must be divided to get a perfect square?
17. 17.A square garden has an area of 2500 square m. How long is each side (in m)?
18. 18.What is 36²? =
19. 19.What is the smallest whole number by which 640 must be divided to get a perfect square?
20. 20.Which of these is a perfect square? (a) 1643 (b) 1600 (c) 1603
21. 21.Which of these is a perfect square? (a) 225 (b) 233 (c) 237
22. 22.What is the smallest whole number by which 45 must be divided to get a perfect square?
23. 23.What is √4900? =
24. 24.What is the sum of the first 20 odd numbers (1 + 3 + 5 + …)?
25. 25.What is 22²? =
26. 26.What is the sum of the first 22 odd numbers (1 + 3 + 5 + …)?
27. 27.What is √8649? =
28. 28.What is the smallest whole number by which 704 must be divided to get a perfect square?
29. 29.How many whole numbers lie between 45² and 46²?
30. 30.What is the smallest whole number by which 320 must be multiplied to get a perfect square?
31. 31.What is the sum of the first 15 odd numbers (1 + 3 + 5 + …)?
32. 32.Which of these is a perfect square? (a) 356 (b) 324 (c) 325
33. 33.How many whole numbers lie between 12² and 13²?
34. 34.What is 97²? =
35. 35.How many whole numbers lie between 37² and 38²?
36. 36.What is 77²? =
37. 37.Which of these is a perfect square? (a) 729 (b) 778 (c) 739
38. 38.How many whole numbers lie between 8² and 9²?
39. 39.What is 54²? =
40. 40.How many whole numbers lie between 21² and 22²?

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