Class 8 Maths Worksheet: Squares and Square Roots

Maths worksheets lesson 58: Squares and square roots · Set 341 · 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 2401 square m. How long is each side (in m)?
2. 2.What is 43²? =
3. 3.What is the smallest whole number by which 275 must be divided to get a perfect square?
4. 4.What is 28²? =
5. 5.What is √3844? =
6. 6.What is √4489? =
7. 7.What is √625? =
8. 8.What is 25²? =
9. 9.A square garden has an area of 289 square m. How long is each side (in m)?
10. 10.What is 62²? =
11. 11.What is the sum of the first 20 odd numbers (1 + 3 + 5 + …)?
12. 12.What is the smallest whole number by which 250 must be multiplied to get a perfect square?
13. 13.Which of these is a perfect square? (a) 755 (b) 742 (c) 729
14. 14.Which of these is a perfect square? (a) 208 (b) 196 (c) 200
15. 15.What is the sum of the first 13 odd numbers (1 + 3 + 5 + …)?
16. 16.Which of these is a perfect square? (a) 1442 (b) 1374 (c) 1369
17. 17.What is 99²? =
18. 18.A square garden has an area of 441 square m. How long is each side (in m)?
19. 19.What is 15²? =
20. 20.What is the smallest whole number by which 243 must be divided to get a perfect square?
21. 21.What is √5625? =
22. 22.What is the smallest whole number by which 63 must be multiplied to get a perfect square?
23. 23.What is 42²? =
24. 24.Which of these is a perfect square? (a) 1296 (b) 1343 (c) 1314
25. 25.How many whole numbers lie between 44² and 45²?
26. 26.What is √169? =
27. 27.A square garden has an area of 576 square m. How long is each side (in m)?
28. 28.What is the smallest whole number by which 486 must be multiplied to get a perfect square?
29. 29.A square garden has an area of 3249 square m. How long is each side (in m)?
30. 30.What is the sum of the first 10 odd numbers (1 + 3 + 5 + …)?
31. 31.What is 57²? =
32. 32.Which of these is a perfect square? (a) 146 (b) 160 (c) 144
33. 33.What is the sum of the first 23 odd numbers (1 + 3 + 5 + …)?
34. 34.How many whole numbers lie between 22² and 23²?
35. 35.What is the smallest whole number by which 1215 must be divided to get a perfect square?
36. 36.What is 21²? =
37. 37.What is the sum of the first 15 odd numbers (1 + 3 + 5 + …)?
38. 38.What is the smallest whole number by which 52 must be multiplied to get a perfect square?
39. 39.What is √289? =
40. 40.Which of these is a perfect square? (a) 616 (b) 615 (c) 576

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