Class 8 Maths Worksheet: Squares and Square Roots

Maths worksheets lesson 58: Squares and square roots · Set 475 · 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 325 must be divided to get a perfect square?
2. 2.What is the sum of the first 23 odd numbers (1 + 3 + 5 + …)?
3. 3.What is 71²? =
4. 4.What is √144? =
5. 5.A square garden has an area of 2025 square m. How long is each side (in m)?
6. 6.Which of these is a perfect square? (a) 447 (b) 444 (c) 441
7. 7.How many whole numbers lie between 11² and 12²?
8. 8.Which of these is a perfect square? (a) 689 (b) 682 (c) 676
9. 9.Which of these is a perfect square? (a) 740 (b) 754 (c) 729
10. 10.What is √3481? =
11. 11.Which of these is a perfect square? (a) 1494 (b) 1457 (c) 1444
12. 12.What is the sum of the first 22 odd numbers (1 + 3 + 5 + …)?
13. 13.A square garden has an area of 169 square m. How long is each side (in m)?
14. 14.What is the smallest whole number by which 1215 must be multiplied to get a perfect square?
15. 15.What is 36²? =
16. 16.What is the smallest whole number by which 50 must be multiplied to get a perfect square?
17. 17.Which of these is a perfect square? (a) 1440 (b) 1431 (c) 1369
18. 18.What is 86²? =
19. 19.What is √2209? =
20. 20.What is the sum of the first 8 odd numbers (1 + 3 + 5 + …)?
21. 21.What is the sum of the first 28 odd numbers (1 + 3 + 5 + …)?
22. 22.How many whole numbers lie between 46² and 47²?
23. 23.A square garden has an area of 529 square m. How long is each side (in m)?
24. 24.What is the sum of the first 27 odd numbers (1 + 3 + 5 + …)?
25. 25.A square garden has an area of 3600 square m. How long is each side (in m)?
26. 26.What is √2916? =
27. 27.What is the sum of the first 26 odd numbers (1 + 3 + 5 + …)?
28. 28.What is √2704? =
29. 29.What is √7396? =
30. 30.Which of these is a perfect square? (a) 400 (b) 414 (c) 433
31. 31.How many whole numbers lie between 40² and 41²?
32. 32.What is √5184? =
33. 33.What is √7744? =
34. 34.What is the smallest whole number by which 405 must be multiplied to get a perfect square?
35. 35.What is √9409? =
36. 36.What is 75²? =
37. 37.A square garden has an area of 256 square m. How long is each side (in m)?
38. 38.How many whole numbers lie between 42² and 43²?
39. 39.What is the smallest whole number by which 98 must be multiplied to get a perfect square?
40. 40.What is 13²? =

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