Class 8 Maths Worksheet: Squares and Square Roots

Maths worksheets lesson 58: Squares and square roots · Set 581 · 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 √4096? =
2. 2.A square garden has an area of 484 square m. How long is each side (in m)?
3. 3.What is the smallest whole number by which 99 must be multiplied to get a perfect square?
4. 4.What is the sum of the first 23 odd numbers (1 + 3 + 5 + …)?
5. 5.What is the sum of the first 17 odd numbers (1 + 3 + 5 + …)?
6. 6.What is 97²? =
7. 7.What is 26²? =
8. 8.What is √5184? =
9. 9.Which of these is a perfect square? (a) 541 (b) 565 (c) 529
10. 10.What is the sum of the first 14 odd numbers (1 + 3 + 5 + …)?
11. 11.A square garden has an area of 2809 square m. How long is each side (in m)?
12. 12.What is the smallest whole number by which 135 must be multiplied to get a perfect square?
13. 13.A square garden has an area of 1681 square m. How long is each side (in m)?
14. 14.How many whole numbers lie between 33² and 34²?
15. 15.A square garden has an area of 225 square m. How long is each side (in m)?
16. 16.What is the sum of the first 29 odd numbers (1 + 3 + 5 + …)?
17. 17.What is the sum of the first 8 odd numbers (1 + 3 + 5 + …)?
18. 18.What is 85²? =
19. 19.What is 95²? =
20. 20.What is the sum of the first 9 odd numbers (1 + 3 + 5 + …)?
21. 21.What is 78²? =
22. 22.What is the sum of the first 6 odd numbers (1 + 3 + 5 + …)?
23. 23.What is the smallest whole number by which 320 must be multiplied to get a perfect square?
24. 24.What is 29²? =
25. 25.What is the sum of the first 5 odd numbers (1 + 3 + 5 + …)?
26. 26.What is 99²? =
27. 27.What is 93²? =
28. 28.A square garden has an area of 784 square m. How long is each side (in m)?
29. 29.What is 57²? =
30. 30.What is the sum of the first 25 odd numbers (1 + 3 + 5 + …)?
31. 31.What is the smallest whole number by which 27 must be divided to get a perfect square?
32. 32.What is √6889? =
33. 33.How many whole numbers lie between 21² and 22²?
34. 34.A square garden has an area of 196 square m. How long is each side (in m)?
35. 35.What is √625? =
36. 36.What is the sum of the first 22 odd numbers (1 + 3 + 5 + …)?
37. 37.Which of these is a perfect square? (a) 486 (b) 526 (c) 484
38. 38.What is √676? =
39. 39.A square garden has an area of 2116 square m. How long is each side (in m)?
40. 40.Which of these is a perfect square? (a) 1296 (b) 1312 (c) 1331

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