Class 8 Maths Worksheet: Squares and Square Roots

Maths worksheets lesson 58: Squares and square roots · Set 99 · 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 43²? =
2. 2.A square garden has an area of 361 square m. How long is each side (in m)?
3. 3.What is 33²? =
4. 4.What is √4356? =
5. 5.What is the sum of the first 7 odd numbers (1 + 3 + 5 + …)?
6. 6.What is the sum of the first 9 odd numbers (1 + 3 + 5 + …)?
7. 7.What is √256? =
8. 8.What is the sum of the first 5 odd numbers (1 + 3 + 5 + …)?
9. 9.What is the sum of the first 12 odd numbers (1 + 3 + 5 + …)?
10. 10.A square garden has an area of 289 square m. How long is each side (in m)?
11. 11.What is the smallest whole number by which 891 must be divided to get a perfect square?
12. 12.What is √5184? =
13. 13.What is 97²? =
14. 14.What is √3844? =
15. 15.What is the sum of the first 25 odd numbers (1 + 3 + 5 + …)?
16. 16.Which of these is a perfect square? (a) 959 (b) 900 (c) 946
17. 17.A square garden has an area of 25 square m. How long is each side (in m)?
18. 18.A square garden has an area of 64 square m. How long is each side (in m)?
19. 19.What is the smallest whole number by which 80 must be multiplied to get a perfect square?
20. 20.How many whole numbers lie between 5² and 6²?
21. 21.What is the smallest whole number by which 112 must be multiplied to get a perfect square?
22. 22.A square garden has an area of 1521 square m. How long is each side (in m)?
23. 23.Which of these is a perfect square? (a) 1369 (b) 1397 (c) 1371
24. 24.A square garden has an area of 676 square m. How long is each side (in m)?
25. 25.What is 77²? =
26. 26.How many whole numbers lie between 38² and 39²?
27. 27.What is 45²? =
28. 28.What is √7225? =
29. 29.What is √5776? =
30. 30.What is the smallest whole number by which 160 must be multiplied to get a perfect square?
31. 31.What is √3249? =
32. 32.What is 28²? =
33. 33.What is the sum of the first 15 odd numbers (1 + 3 + 5 + …)?
34. 34.What is 23²? =
35. 35.What is √1024? =
36. 36.How many whole numbers lie between 27² and 28²?
37. 37.What is √196? =
38. 38.What is the smallest whole number by which 20 must be divided to get a perfect square?
39. 39.How many whole numbers lie between 28² and 29²?
40. 40.Which of these is a perfect square? (a) 1303 (b) 1296 (c) 1337

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