Class 8 Maths Worksheet: Squares and Square Roots

Maths worksheets lesson 58: Squares and square roots · Set 261 · 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.A square garden has an area of 576 square m. How long is each side (in m)?
2. 2.What is 69²? =
3. 3.What is the smallest whole number by which 45 must be divided to get a perfect square?
4. 4.What is 23²? =
5. 5.Which of these is a perfect square? (a) 1184 (b) 1156 (c) 1200
6. 6.What is the sum of the first 15 odd numbers (1 + 3 + 5 + …)?
7. 7.What is the smallest whole number by which 8 must be divided to get a perfect square?
8. 8.How many whole numbers lie between 27² and 28²?
9. 9.A square garden has an area of 196 square m. How long is each side (in m)?
10. 10.What is the sum of the first 8 odd numbers (1 + 3 + 5 + …)?
11. 11.What is √169? =
12. 12.What is the smallest whole number by which 243 must be multiplied to get a perfect square?
13. 13.A square garden has an area of 400 square m. How long is each side (in m)?
14. 14.How many whole numbers lie between 9² and 10²?
15. 15.How many whole numbers lie between 29² and 30²?
16. 16.How many whole numbers lie between 7² and 8²?
17. 17.What is the sum of the first 25 odd numbers (1 + 3 + 5 + …)?
18. 18.What is the sum of the first 18 odd numbers (1 + 3 + 5 + …)?
19. 19.Which of these is a perfect square? (a) 481 (b) 476 (c) 441
20. 20.What is the smallest whole number by which 810 must be multiplied to get a perfect square?
21. 21.What is √1369? =
22. 22.What is 46²? =
23. 23.What is √2304? =
24. 24.What is 18²? =
25. 25.A square garden has an area of 2401 square m. How long is each side (in m)?
26. 26.What is the sum of the first 19 odd numbers (1 + 3 + 5 + …)?
27. 27.A square garden has an area of 121 square m. How long is each side (in m)?
28. 28.What is the smallest whole number by which 686 must be divided to get a perfect square?
29. 29.What is the sum of the first 22 odd numbers (1 + 3 + 5 + …)?
30. 30.Which of these is a perfect square? (a) 289 (b) 301 (c) 297
31. 31.What is the smallest whole number by which 24 must be divided to get a perfect square?
32. 32.What is the smallest whole number by which 44 must be multiplied to get a perfect square?
33. 33.A square garden has an area of 256 square m. How long is each side (in m)?
34. 34.How many whole numbers lie between 26² and 27²?
35. 35.How many whole numbers lie between 18² and 19²?
36. 36.What is the sum of the first 12 odd numbers (1 + 3 + 5 + …)?
37. 37.A square garden has an area of 1764 square m. How long is each side (in m)?
38. 38.What is 49²? =
39. 39.What is 42²? =
40. 40.What is 63²? =

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