Class 8 Maths Worksheet: Squares and Square Roots

Maths worksheets lesson 58: Squares and square roots · Set 123 · 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 69²? =
2. 2.A square garden has an area of 361 square m. How long is each side (in m)?
3. 3.A square garden has an area of 144 square m. How long is each side (in m)?
4. 4.Which of these is a perfect square? (a) 225 (b) 234 (c) 230
5. 5.What is the sum of the first 19 odd numbers (1 + 3 + 5 + …)?
6. 6.How many whole numbers lie between 15² and 16²?
7. 7.What is 23²? =
8. 8.How many whole numbers lie between 9² and 10²?
9. 9.Which of these is a perfect square? (a) 1460 (b) 1444 (c) 1450
10. 10.What is the sum of the first 18 odd numbers (1 + 3 + 5 + …)?
11. 11.What is 37²? =
12. 12.What is √7921? =
13. 13.Which of these is a perfect square? (a) 690 (b) 676 (c) 707
14. 14.What is the smallest whole number by which 490 must be divided to get a perfect square?
15. 15.What is the smallest whole number by which 99 must be divided to get a perfect square?
16. 16.What is the sum of the first 22 odd numbers (1 + 3 + 5 + …)?
17. 17.What is √144? =
18. 18.Which of these is a perfect square? (a) 421 (b) 426 (c) 400
19. 19.What is √6084? =
20. 20.What is the smallest whole number by which 27 must be divided to get a perfect square?
21. 21.Which of these is a perfect square? (a) 121 (b) 122 (c) 137
22. 22.What is √3249? =
23. 23.A square garden has an area of 196 square m. How long is each side (in m)?
24. 24.What is the sum of the first 26 odd numbers (1 + 3 + 5 + …)?
25. 25.How many whole numbers lie between 35² and 36²?
26. 26.What is 95²? =
27. 27.What is 19²? =
28. 28.What is the sum of the first 27 odd numbers (1 + 3 + 5 + …)?
29. 29.A square garden has an area of 3600 square m. How long is each side (in m)?
30. 30.How many whole numbers lie between 14² and 15²?
31. 31.What is the smallest whole number by which 90 must be multiplied to get a perfect square?
32. 32.What is the smallest whole number by which 735 must be multiplied to get a perfect square?
33. 33.What is 16²? =
34. 34.How many whole numbers lie between 40² and 41²?
35. 35.What is 97²? =
36. 36.What is √441? =
37. 37.A square garden has an area of 2916 square m. How long is each side (in m)?
38. 38.A square garden has an area of 324 square m. How long is each side (in m)?
39. 39.A square garden has an area of 2704 square m. How long is each side (in m)?
40. 40.What is 25²? =

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