Class 8 Maths Worksheet: Squares and Square Roots

Maths worksheets lesson 58: Squares and square roots · Set 527 · 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.Which of these is a perfect square? (a) 553 (b) 529 (c) 551
2. 2.What is √5041? =
3. 3.What is 22²? =
4. 4.How many whole numbers lie between 33² and 34²?
5. 5.What is the sum of the first 16 odd numbers (1 + 3 + 5 + …)?
6. 6.A square garden has an area of 1444 square m. How long is each side (in m)?
7. 7.What is the sum of the first 7 odd numbers (1 + 3 + 5 + …)?
8. 8.What is the smallest whole number by which 27 must be multiplied to get a perfect square?
9. 9.What is the sum of the first 18 odd numbers (1 + 3 + 5 + …)?
10. 10.A square garden has an area of 576 square m. How long is each side (in m)?
11. 11.How many whole numbers lie between 49² and 50²?
12. 12.How many whole numbers lie between 9² and 10²?
13. 13.What is the smallest whole number by which 243 must be multiplied to get a perfect square?
14. 14.A square garden has an area of 169 square m. How long is each side (in m)?
15. 15.What is 25²? =
16. 16.What is the smallest whole number by which 27 must be divided to get a perfect square?
17. 17.A square garden has an area of 2916 square m. How long is each side (in m)?
18. 18.What is the sum of the first 28 odd numbers (1 + 3 + 5 + …)?
19. 19.How many whole numbers lie between 47² and 48²?
20. 20.What is the smallest whole number by which 208 must be multiplied to get a perfect square?
21. 21.What is the sum of the first 14 odd numbers (1 + 3 + 5 + …)?
22. 22.What is 37²? =
23. 23.What is 35²? =
24. 24.A square garden has an area of 196 square m. How long is each side (in m)?
25. 25.A square garden has an area of 64 square m. How long is each side (in m)?
26. 26.What is the sum of the first 20 odd numbers (1 + 3 + 5 + …)?
27. 27.What is √625? =
28. 28.A square garden has an area of 2304 square m. How long is each side (in m)?
29. 29.What is √9025? =
30. 30.What is the smallest whole number by which 24 must be divided to get a perfect square?
31. 31.What is √289? =
32. 32.Which of these is a perfect square? (a) 1193 (b) 1156 (c) 1171
33. 33.What is the sum of the first 5 odd numbers (1 + 3 + 5 + …)?
34. 34.What is the sum of the first 19 odd numbers (1 + 3 + 5 + …)?
35. 35.What is √4225? =
36. 36.What is the sum of the first 11 odd numbers (1 + 3 + 5 + …)?
37. 37.What is √2209? =
38. 38.How many whole numbers lie between 8² and 9²?
39. 39.How many whole numbers lie between 16² and 17²?
40. 40.Which of these is a perfect square? (a) 1288 (b) 1225 (c) 1235

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