Class 8 Maths Worksheet: Squares and Square Roots

Maths worksheets lesson 58: Squares and square roots · Set 501 · 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 the sum of the first 18 odd numbers (1 + 3 + 5 + …)?
2. 2.What is the smallest whole number by which 28 must be divided to get a perfect square?
3. 3.What is √529? =
4. 4.How many whole numbers lie between 50² and 51²?
5. 5.What is the smallest whole number by which 896 must be divided to get a perfect square?
6. 6.What is √2116? =
7. 7.Which of these is a perfect square? (a) 144 (b) 152 (c) 148
8. 8.A square garden has an area of 784 square m. How long is each side (in m)?
9. 9.Which of these is a perfect square? (a) 336 (b) 324 (c) 327
10. 10.What is √625? =
11. 11.What is √8100? =
12. 12.What is 75²? =
13. 13.What is the smallest whole number by which 325 must be divided to get a perfect square?
14. 14.What is 90²? =
15. 15.Which of these is a perfect square? (a) 179 (b) 169 (c) 172
16. 16.What is 38²? =
17. 17.What is √4761? =
18. 18.What is the smallest whole number by which 240 must be multiplied to get a perfect square?
19. 19.How many whole numbers lie between 36² and 37²?
20. 20.How many whole numbers lie between 48² and 49²?
21. 21.What is the smallest whole number by which 72 must be divided to get a perfect square?
22. 22.What is 82²? =
23. 23.What is the smallest whole number by which 54 must be divided to get a perfect square?
24. 24.What is the smallest whole number by which 640 must be divided to get a perfect square?
25. 25.What is √324? =
26. 26.How many whole numbers lie between 10² and 11²?
27. 27.What is the smallest whole number by which 117 must be multiplied to get a perfect square?
28. 28.A square garden has an area of 324 square m. How long is each side (in m)?
29. 29.Which of these is a perfect square? (a) 578 (b) 576 (c) 622
30. 30.What is 47²? =
31. 31.What is the sum of the first 21 odd numbers (1 + 3 + 5 + …)?
32. 32.What is √5476? =
33. 33.Which of these is a perfect square? (a) 283 (b) 256 (c) 285
34. 34.A square garden has an area of 1369 square m. How long is each side (in m)?
35. 35.A square garden has an area of 400 square m. How long is each side (in m)?
36. 36.What is the smallest whole number by which 12 must be multiplied to get a perfect square?
37. 37.What is √121? =
38. 38.How many whole numbers lie between 13² and 14²?
39. 39.What is the sum of the first 8 odd numbers (1 + 3 + 5 + …)?
40. 40.What is 33²? =

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