Class 8 Maths Worksheet: Squares and Square Roots

Maths worksheets lesson 58: Squares and square roots · Set 735 · 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 15²? =
2. 2.How many whole numbers lie between 49² and 50²?
3. 3.What is √2401? =
4. 4.What is 67²? =
5. 5.What is the sum of the first 9 odd numbers (1 + 3 + 5 + …)?
6. 6.What is the smallest whole number by which 54 must be divided to get a perfect square?
7. 7.What is the sum of the first 19 odd numbers (1 + 3 + 5 + …)?
8. 8.Which of these is a perfect square? (a) 888 (b) 841 (c) 856
9. 9.Which of these is a perfect square? (a) 400 (b) 416 (c) 432
10. 10.A square garden has an area of 529 square m. How long is each side (in m)?
11. 11.What is 61²? =
12. 12.What is the smallest whole number by which 686 must be multiplied to get a perfect square?
13. 13.What is the sum of the first 29 odd numbers (1 + 3 + 5 + …)?
14. 14.What is √5184? =
15. 15.What is √1521? =
16. 16.What is the sum of the first 11 odd numbers (1 + 3 + 5 + …)?
17. 17.What is 22²? =
18. 18.What is √9801? =
19. 19.What is 75²? =
20. 20.What is the sum of the first 18 odd numbers (1 + 3 + 5 + …)?
21. 21.What is the smallest whole number by which 44 must be divided to get a perfect square?
22. 22.What is 86²? =
23. 23.What is the smallest whole number by which 108 must be multiplied to get a perfect square?
24. 24.How many whole numbers lie between 9² and 10²?
25. 25.What is 25²? =
26. 26.What is the sum of the first 22 odd numbers (1 + 3 + 5 + …)?
27. 27.A square garden has an area of 1156 square m. How long is each side (in m)?
28. 28.What is 26²? =
29. 29.Which of these is a perfect square? (a) 1629 (b) 1600 (c) 1613
30. 30.A square garden has an area of 1521 square m. How long is each side (in m)?
31. 31.What is the smallest whole number by which 45 must be multiplied to get a perfect square?
32. 32.Which of these is a perfect square? (a) 690 (b) 676 (c) 723
33. 33.What is √3721? =
34. 34.What is the sum of the first 27 odd numbers (1 + 3 + 5 + …)?
35. 35.A square garden has an area of 64 square m. How long is each side (in m)?
36. 36.Which of these is a perfect square? (a) 472 (b) 453 (c) 441
37. 37.What is the smallest whole number by which 20 must be divided to get a perfect square?
38. 38.What is √1681? =
39. 39.What is the smallest whole number by which 52 must be multiplied to get a perfect square?
40. 40.What is the smallest whole number by which 343 must be multiplied to get a perfect square?

Free maths worksheets lessons, practice and worksheets at talentjr.in/maths-worksheets