Class 8 Maths Worksheet: Squares and Square Roots

Maths worksheets lesson 58: Squares and square roots · Set 317 · 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 56 must be multiplied to get a perfect square?
2. 2.What is √289? =
3. 3.Which of these is a perfect square? (a) 169 (b) 186 (c) 194
4. 4.What is 68²? =
5. 5.What is the sum of the first 21 odd numbers (1 + 3 + 5 + …)?
6. 6.What is 57²? =
7. 7.What is the smallest whole number by which 176 must be multiplied to get a perfect square?
8. 8.What is 22²? =
9. 9.What is √8649? =
10. 10.What is the sum of the first 8 odd numbers (1 + 3 + 5 + …)?
11. 11.What is the smallest whole number by which 147 must be divided to get a perfect square?
12. 12.What is 83²? =
13. 13.A square garden has an area of 225 square m. How long is each side (in m)?
14. 14.What is 52²? =
15. 15.A square garden has an area of 2401 square m. How long is each side (in m)?
16. 16.A square garden has an area of 3025 square m. How long is each side (in m)?
17. 17.Which of these is a perfect square? (a) 466 (b) 473 (c) 441
18. 18.What is 39²? =
19. 19.What is the sum of the first 14 odd numbers (1 + 3 + 5 + …)?
20. 20.What is the sum of the first 22 odd numbers (1 + 3 + 5 + …)?
21. 21.What is the sum of the first 24 odd numbers (1 + 3 + 5 + …)?
22. 22.What is the smallest whole number by which 735 must be multiplied to get a perfect square?
23. 23.What is 35²? =
24. 24.What is √2601? =
25. 25.How many whole numbers lie between 31² and 32²?
26. 26.A square garden has an area of 961 square m. How long is each side (in m)?
27. 27.A square garden has an area of 3136 square m. How long is each side (in m)?
28. 28.What is 18²? =
29. 29.What is 82²? =
30. 30.How many whole numbers lie between 32² and 33²?
31. 31.What is 99²? =
32. 32.A square garden has an area of 1024 square m. How long is each side (in m)?
33. 33.What is √676? =
34. 34.How many whole numbers lie between 30² and 31²?
35. 35.What is 74²? =
36. 36.What is the smallest whole number by which 99 must be divided to get a perfect square?
37. 37.What is the smallest whole number by which 40 must be divided to get a perfect square?
38. 38.Which of these is a perfect square? (a) 890 (b) 880 (c) 841
39. 39.What is √3249? =
40. 40.Which of these is a perfect square? (a) 771 (b) 763 (c) 729

Free maths worksheets lessons, practice and worksheets at talentjr.in/maths-worksheets