Class 8 Maths Worksheet: Squares and Square Roots

Maths worksheets lesson 58: Squares and square roots · Set 128 · 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.A square garden has an area of 676 square m. How long is each side (in m)?
2. 2.What is √4761? =
3. 3.What is 53²? =
4. 4.A square garden has an area of 1936 square m. How long is each side (in m)?
5. 5.How many whole numbers lie between 50² and 51²?
6. 6.What is 35²? =
7. 7.What is the sum of the first 15 odd numbers (1 + 3 + 5 + …)?
8. 8.Which of these is a perfect square? (a) 1616 (b) 1669 (c) 1600
9. 9.A square garden has an area of 784 square m. How long is each side (in m)?
10. 10.What is the smallest whole number by which 396 must be multiplied to get a perfect square?
11. 11.What is √1849? =
12. 12.Which of these is a perfect square? (a) 1421 (b) 1372 (c) 1369
13. 13.Which of these is a perfect square? (a) 128 (b) 121 (c) 139
14. 14.What is the sum of the first 17 odd numbers (1 + 3 + 5 + …)?
15. 15.What is √625? =
16. 16.What is 27²? =
17. 17.Which of these is a perfect square? (a) 1532 (b) 1527 (c) 1521
18. 18.A square garden has an area of 2601 square m. How long is each side (in m)?
19. 19.What is the smallest whole number by which 1134 must be divided to get a perfect square?
20. 20.Which of these is a perfect square? (a) 510 (b) 484 (c) 494
21. 21.What is √8836? =
22. 22.What is the sum of the first 29 odd numbers (1 + 3 + 5 + …)?
23. 23.What is the sum of the first 11 odd numbers (1 + 3 + 5 + …)?
24. 24.How many whole numbers lie between 49² and 50²?
25. 25.What is the sum of the first 30 odd numbers (1 + 3 + 5 + …)?
26. 26.What is √729? =
27. 27.What is the smallest whole number by which 99 must be multiplied to get a perfect square?
28. 28.What is the sum of the first 16 odd numbers (1 + 3 + 5 + …)?
29. 29.What is √8649? =
30. 30.How many whole numbers lie between 48² and 49²?
31. 31.What is the sum of the first 21 odd numbers (1 + 3 + 5 + …)?
32. 32.What is √7396? =
33. 33.What is the sum of the first 5 odd numbers (1 + 3 + 5 + …)?
34. 34.What is the sum of the first 9 odd numbers (1 + 3 + 5 + …)?
35. 35.What is √1444? =
36. 36.How many whole numbers lie between 22² and 23²?
37. 37.What is √9025? =
38. 38.What is the sum of the first 20 odd numbers (1 + 3 + 5 + …)?
39. 39.What is the smallest whole number by which 150 must be divided to get a perfect square?
40. 40.A square garden has an area of 100 square m. How long is each side (in m)?

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