Class 8 Maths Worksheet: Squares and Square Roots

Maths worksheets lesson 58: Squares and square roots · Set 573 · 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 36 square m. How long is each side (in m)?
2. 2.A square garden has an area of 2401 square m. How long is each side (in m)?
3. 3.What is the sum of the first 13 odd numbers (1 + 3 + 5 + …)?
4. 4.Which of these is a perfect square? (a) 961 (b) 972 (c) 1019
5. 5.What is 89²? =
6. 6.What is √1444? =
7. 7.What is the sum of the first 23 odd numbers (1 + 3 + 5 + …)?
8. 8.What is 76²? =
9. 9.What is the sum of the first 14 odd numbers (1 + 3 + 5 + …)?
10. 10.What is 63²? =
11. 11.What is the sum of the first 18 odd numbers (1 + 3 + 5 + …)?
12. 12.How many whole numbers lie between 5² and 6²?
13. 13.Which of these is a perfect square? (a) 1375 (b) 1395 (c) 1369
14. 14.How many whole numbers lie between 39² and 40²?
15. 15.What is the smallest whole number by which 490 must be divided to get a perfect square?
16. 16.A square garden has an area of 784 square m. How long is each side (in m)?
17. 17.What is the sum of the first 6 odd numbers (1 + 3 + 5 + …)?
18. 18.What is the smallest whole number by which 98 must be divided to get a perfect square?
19. 19.What is the sum of the first 22 odd numbers (1 + 3 + 5 + …)?
20. 20.Which of these is a perfect square? (a) 676 (b) 702 (c) 685
21. 21.What is 54²? =
22. 22.Which of these is a perfect square? (a) 542 (b) 536 (c) 529
23. 23.A square garden has an area of 1024 square m. How long is each side (in m)?
24. 24.What is 97²? =
25. 25.What is 56²? =
26. 26.A square garden has an area of 961 square m. How long is each side (in m)?
27. 27.What is 67²? =
28. 28.What is 26²? =
29. 29.What is √2809? =
30. 30.What is 32²? =
31. 31.What is √9216? =
32. 32.A square garden has an area of 289 square m. How long is each side (in m)?
33. 33.What is the sum of the first 12 odd numbers (1 + 3 + 5 + …)?
34. 34.What is the smallest whole number by which 108 must be multiplied to get a perfect square?
35. 35.How many whole numbers lie between 18² and 19²?
36. 36.How many whole numbers lie between 6² and 7²?
37. 37.What is the smallest whole number by which 128 must be multiplied to get a perfect square?
38. 38.A square garden has an area of 1225 square m. How long is each side (in m)?
39. 39.Which of these is a perfect square? (a) 236 (b) 225 (c) 252
40. 40.How many whole numbers lie between 37² and 38²?

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