Class 8 Maths Worksheet: Squares and Square Roots

Maths worksheets lesson 58: Squares and square roots · Set 212 · 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 35²? =
2. 2.What is √576? =
3. 3.What is 89²? =
4. 4.A square garden has an area of 361 square m. How long is each side (in m)?
5. 5.What is the smallest whole number by which 45 must be multiplied to get a perfect square?
6. 6.How many whole numbers lie between 32² and 33²?
7. 7.What is the smallest whole number by which 117 must be multiplied to get a perfect square?
8. 8.What is 77²? =
9. 9.What is 25²? =
10. 10.What is √5329? =
11. 11.What is the smallest whole number by which 448 must be multiplied to get a perfect square?
12. 12.What is 76²? =
13. 13.What is √256? =
14. 14.Which of these is a perfect square? (a) 183 (b) 169 (c) 184
15. 15.What is 67²? =
16. 16.What is the sum of the first 7 odd numbers (1 + 3 + 5 + …)?
17. 17.What is the sum of the first 26 odd numbers (1 + 3 + 5 + …)?
18. 18.Which of these is a perfect square? (a) 344 (b) 333 (c) 324
19. 19.What is the sum of the first 15 odd numbers (1 + 3 + 5 + …)?
20. 20.What is √1444? =
21. 21.What is the sum of the first 20 odd numbers (1 + 3 + 5 + …)?
22. 22.Which of these is a perfect square? (a) 563 (b) 529 (c) 533
23. 23.What is √2401? =
24. 24.What is the smallest whole number by which 28 must be multiplied to get a perfect square?
25. 25.A square garden has an area of 25 square m. How long is each side (in m)?
26. 26.What is the sum of the first 18 odd numbers (1 + 3 + 5 + …)?
27. 27.A square garden has an area of 324 square m. How long is each side (in m)?
28. 28.How many whole numbers lie between 8² and 9²?
29. 29.How many whole numbers lie between 9² and 10²?
30. 30.What is 18²? =
31. 31.What is 81²? =
32. 32.What is the sum of the first 29 odd numbers (1 + 3 + 5 + …)?
33. 33.What is √2500? =
34. 34.Which of these is a perfect square? (a) 584 (b) 580 (c) 576
35. 35.How many whole numbers lie between 46² and 47²?
36. 36.What is the smallest whole number by which 60 must be multiplied to get a perfect square?
37. 37.Which of these is a perfect square? (a) 1672 (b) 1679 (c) 1600
38. 38.What is the sum of the first 19 odd numbers (1 + 3 + 5 + …)?
39. 39.What is the smallest whole number by which 108 must be divided to get a perfect square?
40. 40.What is the smallest whole number by which 1215 must be multiplied to get a perfect square?

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