Class 8 Maths Worksheet: Squares and Square Roots

Maths worksheets lesson 58: Squares and square roots · Set 331 · 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 sum of the first 24 odd numbers (1 + 3 + 5 + …)?
2. 2.How many whole numbers lie between 48² and 49²?
3. 3.What is the smallest whole number by which 44 must be divided to get a perfect square?
4. 4.What is the smallest whole number by which 192 must be multiplied to get a perfect square?
5. 5.What is the smallest whole number by which 150 must be divided to get a perfect square?
6. 6.What is 27²? =
7. 7.What is the sum of the first 18 odd numbers (1 + 3 + 5 + …)?
8. 8.A square garden has an area of 441 square m. How long is each side (in m)?
9. 9.What is √2601? =
10. 10.What is the smallest whole number by which 8 must be multiplied to get a perfect square?
11. 11.A square garden has an area of 1156 square m. How long is each side (in m)?
12. 12.A square garden has an area of 676 square m. How long is each side (in m)?
13. 13.A square garden has an area of 1024 square m. How long is each side (in m)?
14. 14.What is the sum of the first 20 odd numbers (1 + 3 + 5 + …)?
15. 15.What is the sum of the first 28 odd numbers (1 + 3 + 5 + …)?
16. 16.What is the smallest whole number by which 704 must be multiplied to get a perfect square?
17. 17.Which of these is a perfect square? (a) 1515 (b) 1444 (c) 1472
18. 18.What is 75²? =
19. 19.What is √1089? =
20. 20.What is 99²? =
21. 21.Which of these is a perfect square? (a) 865 (b) 841 (c) 861
22. 22.What is √7225? =
23. 23.What is the smallest whole number by which 448 must be multiplied to get a perfect square?
24. 24.What is 80²? =
25. 25.What is √4225? =
26. 26.A square garden has an area of 81 square m. How long is each side (in m)?
27. 27.What is √9216? =
28. 28.How many whole numbers lie between 9² and 10²?
29. 29.What is 11²? =
30. 30.What is 31²? =
31. 31.What is 32²? =
32. 32.What is 49²? =
33. 33.What is the sum of the first 25 odd numbers (1 + 3 + 5 + …)?
34. 34.A square garden has an area of 2401 square m. How long is each side (in m)?
35. 35.Which of these is a perfect square? (a) 196 (b) 214 (c) 202
36. 36.What is 14²? =
37. 37.What is the smallest whole number by which 128 must be divided to get a perfect square?
38. 38.What is √484? =
39. 39.Which of these is a perfect square? (a) 324 (b) 349 (c) 359
40. 40.Which of these is a perfect square? (a) 833 (b) 784 (c) 832

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