Class 8 Maths Worksheet: Squares and Square Roots

Maths worksheets lesson 58: Squares and square roots · Set 435 · 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 400 square m. How long is each side (in m)?
2. 2.What is √8836? =
3. 3.How many whole numbers lie between 9² and 10²?
4. 4.Which of these is a perfect square? (a) 823 (b) 815 (c) 784
5. 5.What is the smallest whole number by which 208 must be divided to get a perfect square?
6. 6.What is √400? =
7. 7.What is √1225? =
8. 8.How many whole numbers lie between 7² and 8²?
9. 9.What is 97²? =
10. 10.What is the sum of the first 5 odd numbers (1 + 3 + 5 + …)?
11. 11.What is the smallest whole number by which 32 must be divided to get a perfect square?
12. 12.Which of these is a perfect square? (a) 256 (b) 271 (c) 257
13. 13.What is √2025? =
14. 14.What is √4624? =
15. 15.What is √1681? =
16. 16.What is the smallest whole number by which 486 must be divided to get a perfect square?
17. 17.What is 19²? =
18. 18.What is √5476? =
19. 19.What is the smallest whole number by which 108 must be multiplied to get a perfect square?
20. 20.Which of these is a perfect square? (a) 497 (b) 484 (c) 492
21. 21.What is the sum of the first 19 odd numbers (1 + 3 + 5 + …)?
22. 22.What is the smallest whole number by which 540 must be multiplied to get a perfect square?
23. 23.What is the sum of the first 7 odd numbers (1 + 3 + 5 + …)?
24. 24.What is the sum of the first 15 odd numbers (1 + 3 + 5 + …)?
25. 25.Which of these is a perfect square? (a) 1067 (b) 1024 (c) 1071
26. 26.How many whole numbers lie between 39² and 40²?
27. 27.What is 74²? =
28. 28.What is √6241? =
29. 29.What is √841? =
30. 30.A square garden has an area of 64 square m. How long is each side (in m)?
31. 31.Which of these is a perfect square? (a) 104 (b) 108 (c) 100
32. 32.Which of these is a perfect square? (a) 1467 (b) 1478 (c) 1444
33. 33.What is 67²? =
34. 34.How many whole numbers lie between 24² and 25²?
35. 35.Which of these is a perfect square? (a) 1369 (b) 1384 (c) 1439
36. 36.How many whole numbers lie between 15² and 16²?
37. 37.What is the smallest whole number by which 54 must be multiplied to get a perfect square?
38. 38.What is the smallest whole number by which 180 must be multiplied to get a perfect square?
39. 39.What is the smallest whole number by which 48 must be divided to get a perfect square?
40. 40.What is the smallest whole number by which 252 must be divided to get a perfect square?

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