Class 8 Maths Worksheet: Squares and Square Roots

Maths worksheets lesson 58: Squares and square roots · Set 478 · 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 20 odd numbers (1 + 3 + 5 + …)?
2. 2.How many whole numbers lie between 45² and 46²?
3. 3.What is 99²? =
4. 4.How many whole numbers lie between 39² and 40²?
5. 5.A square garden has an area of 1296 square m. How long is each side (in m)?
6. 6.What is √6241? =
7. 7.What is √5476? =
8. 8.What is √1936? =
9. 9.What is √4489? =
10. 10.What is the sum of the first 17 odd numbers (1 + 3 + 5 + …)?
11. 11.How many whole numbers lie between 6² and 7²?
12. 12.What is the sum of the first 25 odd numbers (1 + 3 + 5 + …)?
13. 13.What is the sum of the first 30 odd numbers (1 + 3 + 5 + …)?
14. 14.What is √6561? =
15. 15.Which of these is a perfect square? (a) 494 (b) 512 (c) 484
16. 16.How many whole numbers lie between 19² and 20²?
17. 17.A square garden has an area of 1600 square m. How long is each side (in m)?
18. 18.What is 72²? =
19. 19.What is √9025? =
20. 20.What is √625? =
21. 21.What is 61²? =
22. 22.What is the sum of the first 24 odd numbers (1 + 3 + 5 + …)?
23. 23.What is √289? =
24. 24.What is the smallest whole number by which 896 must be multiplied to get a perfect square?
25. 25.What is the smallest whole number by which 128 must be multiplied to get a perfect square?
26. 26.How many whole numbers lie between 5² and 6²?
27. 27.A square garden has an area of 1156 square m. How long is each side (in m)?
28. 28.A square garden has an area of 324 square m. How long is each side (in m)?
29. 29.A square garden has an area of 900 square m. How long is each side (in m)?
30. 30.What is the smallest whole number by which 32 must be divided to get a perfect square?
31. 31.Which of these is a perfect square? (a) 1404 (b) 1369 (c) 1417
32. 32.Which of these is a perfect square? (a) 184 (b) 169 (c) 188
33. 33.What is the smallest whole number by which 98 must be multiplied to get a perfect square?
34. 34.Which of these is a perfect square? (a) 1291 (b) 1225 (c) 1230
35. 35.Which of these is a perfect square? (a) 969 (b) 984 (c) 961
36. 36.What is the smallest whole number by which 245 must be multiplied to get a perfect square?
37. 37.What is the smallest whole number by which 28 must be multiplied to get a perfect square?
38. 38.A square garden has an area of 2500 square m. How long is each side (in m)?
39. 39.What is 93²? =
40. 40.What is √144? =

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