Class 8 Maths Worksheet: Squares and Square Roots

Maths worksheets lesson 58: Squares and square roots · Set 353 · 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 √3136? =
2. 2.Which of these is a perfect square? (a) 289 (b) 309 (c) 292
3. 3.A square garden has an area of 36 square m. How long is each side (in m)?
4. 4.A square garden has an area of 2401 square m. How long is each side (in m)?
5. 5.How many whole numbers lie between 47² and 48²?
6. 6.Which of these is a perfect square? (a) 266 (b) 270 (c) 256
7. 7.Which of these is a perfect square? (a) 1225 (b) 1278 (c) 1287
8. 8.What is the sum of the first 19 odd numbers (1 + 3 + 5 + …)?
9. 9.How many whole numbers lie between 39² and 40²?
10. 10.What is the smallest whole number by which 320 must be divided to get a perfect square?
11. 11.What is 93²? =
12. 12.What is the sum of the first 9 odd numbers (1 + 3 + 5 + …)?
13. 13.What is the smallest whole number by which 180 must be multiplied to get a perfect square?
14. 14.What is the sum of the first 26 odd numbers (1 + 3 + 5 + …)?
15. 15.What is 25²? =
16. 16.How many whole numbers lie between 43² and 44²?
17. 17.Which of these is a perfect square? (a) 563 (b) 552 (c) 529
18. 18.Which of these is a perfect square? (a) 364 (b) 361 (c) 397
19. 19.Which of these is a perfect square? (a) 225 (b) 229 (c) 244
20. 20.What is √4489? =
21. 21.What is √6241? =
22. 22.What is the smallest whole number by which 540 must be multiplied to get a perfect square?
23. 23.A square garden has an area of 676 square m. How long is each side (in m)?
24. 24.What is the sum of the first 15 odd numbers (1 + 3 + 5 + …)?
25. 25.What is √1600? =
26. 26.A square garden has an area of 2209 square m. How long is each side (in m)?
27. 27.What is √7056? =
28. 28.What is the smallest whole number by which 504 must be divided to get a perfect square?
29. 29.What is the smallest whole number by which 832 must be divided to get a perfect square?
30. 30.What is √3481? =
31. 31.What is the smallest whole number by which 99 must be divided to get a perfect square?
32. 32.What is the sum of the first 8 odd numbers (1 + 3 + 5 + …)?
33. 33.What is √225? =
34. 34.What is √121? =
35. 35.A square garden has an area of 1089 square m. How long is each side (in m)?
36. 36.What is the sum of the first 5 odd numbers (1 + 3 + 5 + …)?
37. 37.What is √324? =
38. 38.What is the smallest whole number by which 12 must be divided to get a perfect square?
39. 39.What is √9801? =
40. 40.What is 73²? =

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