Class 8 Maths Worksheet: Squares and Square Roots

Maths worksheets lesson 58: Squares and square roots · Set 380 · 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 73²? =
2. 2.Which of these is a perfect square? (a) 655 (b) 664 (c) 625
3. 3.A square garden has an area of 324 square m. How long is each side (in m)?
4. 4.What is √3600? =
5. 5.What is √5184? =
6. 6.What is the sum of the first 6 odd numbers (1 + 3 + 5 + …)?
7. 7.What is 56²? =
8. 8.Which of these is a perfect square? (a) 256 (b) 258 (c) 263
9. 9.What is 75²? =
10. 10.What is 19²? =
11. 11.What is √5929? =
12. 12.A square garden has an area of 1024 square m. How long is each side (in m)?
13. 13.What is √5625? =
14. 14.What is the sum of the first 10 odd numbers (1 + 3 + 5 + …)?
15. 15.What is the sum of the first 14 odd numbers (1 + 3 + 5 + …)?
16. 16.How many whole numbers lie between 19² and 20²?
17. 17.Which of these is a perfect square? (a) 794 (b) 839 (c) 784
18. 18.What is √5041? =
19. 19.A square garden has an area of 1444 square m. How long is each side (in m)?
20. 20.What is √6889? =
21. 21.What is √8649? =
22. 22.What is the sum of the first 11 odd numbers (1 + 3 + 5 + …)?
23. 23.What is the sum of the first 16 odd numbers (1 + 3 + 5 + …)?
24. 24.What is the sum of the first 23 odd numbers (1 + 3 + 5 + …)?
25. 25.Which of these is a perfect square? (a) 1444 (b) 1448 (c) 1472
26. 26.What is 45²? =
27. 27.What is √9409? =
28. 28.How many whole numbers lie between 37² and 38²?
29. 29.What is the smallest whole number by which 32 must be multiplied to get a perfect square?
30. 30.What is 96²? =
31. 31.What is 46²? =
32. 32.Which of these is a perfect square? (a) 1025 (b) 1032 (c) 1024
33. 33.What is the smallest whole number by which 245 must be multiplied to get a perfect square?
34. 34.What is 44²? =
35. 35.What is the sum of the first 19 odd numbers (1 + 3 + 5 + …)?
36. 36.Which of these is a perfect square? (a) 576 (b) 589 (c) 587
37. 37.What is the smallest whole number by which 275 must be divided to get a perfect square?
38. 38.What is the sum of the first 21 odd numbers (1 + 3 + 5 + …)?
39. 39.How many whole numbers lie between 12² and 13²?
40. 40.What is 86²? =

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