Class 8 Maths Worksheet: Squares and Square Roots

Maths worksheets lesson 58: Squares and square roots · Set 187 · 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 24 odd numbers (1 + 3 + 5 + …)?
2. 2.What is the sum of the first 15 odd numbers (1 + 3 + 5 + …)?
3. 3.What is the sum of the first 10 odd numbers (1 + 3 + 5 + …)?
4. 4.What is 23²? =
5. 5.What is √841? =
6. 6.How many whole numbers lie between 46² and 47²?
7. 7.What is √1936? =
8. 8.What is the sum of the first 30 odd numbers (1 + 3 + 5 + …)?
9. 9.What is the sum of the first 25 odd numbers (1 + 3 + 5 + …)?
10. 10.What is 70²? =
11. 11.What is 98²? =
12. 12.What is the smallest whole number by which 75 must be multiplied to get a perfect square?
13. 13.What is 75²? =
14. 14.Which of these is a perfect square? (a) 184 (b) 169 (c) 173
15. 15.Which of these is a perfect square? (a) 413 (b) 436 (c) 400
16. 16.What is the smallest whole number by which 180 must be multiplied to get a perfect square?
17. 17.What is √4761? =
18. 18.What is the sum of the first 26 odd numbers (1 + 3 + 5 + …)?
19. 19.A square garden has an area of 1936 square m. How long is each side (in m)?
20. 20.How many whole numbers lie between 21² and 22²?
21. 21.What is 95²? =
22. 22.How many whole numbers lie between 24² and 25²?
23. 23.Which of these is a perfect square? (a) 1188 (b) 1171 (c) 1156
24. 24.A square garden has an area of 2304 square m. How long is each side (in m)?
25. 25.How many whole numbers lie between 13² and 14²?
26. 26.What is √1225? =
27. 27.What is the sum of the first 5 odd numbers (1 + 3 + 5 + …)?
28. 28.A square garden has an area of 324 square m. How long is each side (in m)?
29. 29.What is √2025? =
30. 30.What is the sum of the first 29 odd numbers (1 + 3 + 5 + …)?
31. 31.What is 68²? =
32. 32.What is 14²? =
33. 33.What is the smallest whole number by which 504 must be multiplied to get a perfect square?
34. 34.A square garden has an area of 2704 square m. How long is each side (in m)?
35. 35.A square garden has an area of 676 square m. How long is each side (in m)?
36. 36.What is √1156? =
37. 37.Which of these is a perfect square? (a) 588 (b) 576 (c) 600
38. 38.What is √361? =
39. 39.How many whole numbers lie between 31² and 32²?
40. 40.Which of these is a perfect square? (a) 121 (b) 139 (c) 143

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