Class 8 Maths Worksheet: Squares and Square Roots

Maths worksheets lesson 58: Squares and square roots · Set 728 · 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 34²? =
2. 2.What is the smallest whole number by which 320 must be multiplied to get a perfect square?
3. 3.What is 64²? =
4. 4.What is the sum of the first 6 odd numbers (1 + 3 + 5 + …)?
5. 5.What is √3249? =
6. 6.What is the smallest whole number by which 80 must be multiplied to get a perfect square?
7. 7.What is the smallest whole number by which 486 must be multiplied to get a perfect square?
8. 8.Which of these is a perfect square? (a) 282 (b) 279 (c) 256
9. 9.Which of these is a perfect square? (a) 691 (b) 727 (c) 676
10. 10.What is 14²? =
11. 11.Which of these is a perfect square? (a) 196 (b) 203 (c) 205
12. 12.What is √400? =
13. 13.A square garden has an area of 2304 square m. How long is each side (in m)?
14. 14.What is √4356? =
15. 15.What is the sum of the first 20 odd numbers (1 + 3 + 5 + …)?
16. 16.Which of these is a perfect square? (a) 821 (b) 784 (c) 834
17. 17.What is the smallest whole number by which 8 must be multiplied to get a perfect square?
18. 18.What is the sum of the first 14 odd numbers (1 + 3 + 5 + …)?
19. 19.What is 47²? =
20. 20.What is the smallest whole number by which 72 must be divided to get a perfect square?
21. 21.What is the smallest whole number by which 896 must be divided to get a perfect square?
22. 22.How many whole numbers lie between 47² and 48²?
23. 23.What is 17²? =
24. 24.Which of these is a perfect square? (a) 900 (b) 944 (c) 926
25. 25.How many whole numbers lie between 19² and 20²?
26. 26.How many whole numbers lie between 14² and 15²?
27. 27.A square garden has an area of 900 square m. How long is each side (in m)?
28. 28.What is 28²? =
29. 29.What is the smallest whole number by which 60 must be divided to get a perfect square?
30. 30.What is the smallest whole number by which 125 must be multiplied to get a perfect square?
31. 31.What is 29²? =
32. 32.What is 67²? =
33. 33.A square garden has an area of 144 square m. How long is each side (in m)?
34. 34.What is the smallest whole number by which 56 must be divided to get a perfect square?
35. 35.A square garden has an area of 1681 square m. How long is each side (in m)?
36. 36.What is 59²? =
37. 37.What is the smallest whole number by which 40 must be divided to get a perfect square?
38. 38.A square garden has an area of 324 square m. How long is each side (in m)?
39. 39.How many whole numbers lie between 13² and 14²?
40. 40.What is √784? =

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