Class 8 Maths Worksheet: Squares and Square Roots

Maths worksheets lesson 58: Squares and square roots · Set 82 · 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 87²? =
2. 2.What is √1225? =
3. 3.What is the sum of the first 23 odd numbers (1 + 3 + 5 + …)?
4. 4.What is the sum of the first 15 odd numbers (1 + 3 + 5 + …)?
5. 5.Which of these is a perfect square? (a) 946 (b) 900 (c) 917
6. 6.What is √2025? =
7. 7.What is the smallest whole number by which 180 must be divided to get a perfect square?
8. 8.Which of these is a perfect square? (a) 1413 (b) 1388 (c) 1369
9. 9.Which of these is a perfect square? (a) 858 (b) 851 (c) 841
10. 10.What is √9604? =
11. 11.How many whole numbers lie between 25² and 26²?
12. 12.What is √6241? =
13. 13.What is the sum of the first 12 odd numbers (1 + 3 + 5 + …)?
14. 14.How many whole numbers lie between 28² and 29²?
15. 15.What is 61²? =
16. 16.What is √5776? =
17. 17.How many whole numbers lie between 18² and 19²?
18. 18.A square garden has an area of 2809 square m. How long is each side (in m)?
19. 19.A square garden has an area of 2209 square m. How long is each side (in m)?
20. 20.Which of these is a perfect square? (a) 1605 (b) 1671 (c) 1600
21. 21.How many whole numbers lie between 13² and 14²?
22. 22.What is the sum of the first 17 odd numbers (1 + 3 + 5 + …)?
23. 23.What is the sum of the first 11 odd numbers (1 + 3 + 5 + …)?
24. 24.What is √121? =
25. 25.How many whole numbers lie between 48² and 49²?
26. 26.What is 20²? =
27. 27.What is √4900? =
28. 28.How many whole numbers lie between 34² and 35²?
29. 29.What is the sum of the first 13 odd numbers (1 + 3 + 5 + …)?
30. 30.A square garden has an area of 3025 square m. How long is each side (in m)?
31. 31.What is the sum of the first 5 odd numbers (1 + 3 + 5 + …)?
32. 32.How many whole numbers lie between 44² and 45²?
33. 33.What is the smallest whole number by which 125 must be divided to get a perfect square?
34. 34.A square garden has an area of 144 square m. How long is each side (in m)?
35. 35.What is 33²? =
36. 36.Which of these is a perfect square? (a) 271 (b) 256 (c) 286
37. 37.What is √5929? =
38. 38.What is 74²? =
39. 39.A square garden has an area of 36 square m. How long is each side (in m)?
40. 40.What is the smallest whole number by which 80 must be divided to get a perfect square?

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