Class 8 Maths Worksheet: Squares and Square Roots

Maths worksheets lesson 58: Squares and square roots · Set 343 · 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 49 square m. How long is each side (in m)?
2. 2.How many whole numbers lie between 42² and 43²?
3. 3.A square garden has an area of 2601 square m. How long is each side (in m)?
4. 4.What is 40²? =
5. 5.A square garden has an area of 676 square m. How long is each side (in m)?
6. 6.How many whole numbers lie between 29² and 30²?
7. 7.What is √3249? =
8. 8.What is √256? =
9. 9.What is √2025? =
10. 10.What is the smallest whole number by which 1134 must be divided to get a perfect square?
11. 11.What is the sum of the first 11 odd numbers (1 + 3 + 5 + …)?
12. 12.What is √676? =
13. 13.What is √6889? =
14. 14.How many whole numbers lie between 37² and 38²?
15. 15.What is the sum of the first 20 odd numbers (1 + 3 + 5 + …)?
16. 16.Which of these is a perfect square? (a) 270 (b) 257 (c) 256
17. 17.What is √2704? =
18. 18.What is the smallest whole number by which 539 must be multiplied to get a perfect square?
19. 19.What is the smallest whole number by which 567 must be divided to get a perfect square?
20. 20.What is the sum of the first 19 odd numbers (1 + 3 + 5 + …)?
21. 21.What is 97²? =
22. 22.Which of these is a perfect square? (a) 103 (b) 119 (c) 100
23. 23.What is √361? =
24. 24.What is the sum of the first 28 odd numbers (1 + 3 + 5 + …)?
25. 25.What is the sum of the first 18 odd numbers (1 + 3 + 5 + …)?
26. 26.What is the smallest whole number by which 63 must be multiplied to get a perfect square?
27. 27.A square garden has an area of 100 square m. How long is each side (in m)?
28. 28.What is 83²? =
29. 29.Which of these is a perfect square? (a) 1581 (b) 1583 (c) 1521
30. 30.What is the smallest whole number by which 243 must be multiplied to get a perfect square?
31. 31.What is 41²? =
32. 32.What is 47²? =
33. 33.How many whole numbers lie between 18² and 19²?
34. 34.How many whole numbers lie between 20² and 21²?
35. 35.What is the smallest whole number by which 24 must be multiplied to get a perfect square?
36. 36.Which of these is a perfect square? (a) 366 (b) 361 (c) 364
37. 37.How many whole numbers lie between 24² and 25²?
38. 38.How many whole numbers lie between 7² and 8²?
39. 39.A square garden has an area of 3364 square m. How long is each side (in m)?
40. 40.What is the smallest whole number by which 360 must be divided to get a perfect square?

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