Class 8 Maths Worksheet: Squares and Square Roots

Maths worksheets lesson 58: Squares and square roots · Set 622 · 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 √2209? =
2. 2.What is √5476? =
3. 3.How many whole numbers lie between 7² and 8²?
4. 4.How many whole numbers lie between 27² and 28²?
5. 5.What is the sum of the first 30 odd numbers (1 + 3 + 5 + …)?
6. 6.What is √6241? =
7. 7.What is the smallest whole number by which 224 must be multiplied to get a perfect square?
8. 8.A square garden has an area of 3364 square m. How long is each side (in m)?
9. 9.What is the smallest whole number by which 448 must be divided to get a perfect square?
10. 10.What is the smallest whole number by which 375 must be divided to get a perfect square?
11. 11.What is 36²? =
12. 12.What is the smallest whole number by which 1215 must be multiplied to get a perfect square?
13. 13.What is 38²? =
14. 14.How many whole numbers lie between 19² and 20²?
15. 15.What is √9216? =
16. 16.A square garden has an area of 1521 square m. How long is each side (in m)?
17. 17.How many whole numbers lie between 35² and 36²?
18. 18.How many whole numbers lie between 42² and 43²?
19. 19.What is √2500? =
20. 20.A square garden has an area of 3136 square m. How long is each side (in m)?
21. 21.What is 61²? =
22. 22.How many whole numbers lie between 8² and 9²?
23. 23.What is the smallest whole number by which 108 must be divided to get a perfect square?
24. 24.What is the sum of the first 17 odd numbers (1 + 3 + 5 + …)?
25. 25.What is 69²? =
26. 26.A square garden has an area of 256 square m. How long is each side (in m)?
27. 27.What is 11²? =
28. 28.What is the sum of the first 13 odd numbers (1 + 3 + 5 + …)?
29. 29.Which of these is a perfect square? (a) 1002 (b) 1003 (c) 961
30. 30.What is the sum of the first 7 odd numbers (1 + 3 + 5 + …)?
31. 31.What is the sum of the first 9 odd numbers (1 + 3 + 5 + …)?
32. 32.What is 97²? =
33. 33.What is 20²? =
34. 34.What is 26²? =
35. 35.What is 99²? =
36. 36.What is 72²? =
37. 37.How many whole numbers lie between 46² and 47²?
38. 38.What is 47²? =
39. 39.A square garden has an area of 2401 square m. How long is each side (in m)?
40. 40.How many whole numbers lie between 31² and 32²?

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