Class 8 Maths Worksheet: Squares and Square Roots

Maths worksheets lesson 58: Squares and square roots · Set 618 · 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.A square garden has an area of 256 square m. How long is each side (in m)?
2. 2.A square garden has an area of 841 square m. How long is each side (in m)?
3. 3.What is 77²? =
4. 4.What is 56²? =
5. 5.What is √2304? =
6. 6.What is √961? =
7. 7.What is 74²? =
8. 8.Which of these is a perfect square? (a) 676 (b) 720 (c) 718
9. 9.Which of these is a perfect square? (a) 1056 (b) 1080 (c) 1024
10. 10.What is the smallest whole number by which 128 must be multiplied to get a perfect square?
11. 11.What is 51²? =
12. 12.Which of these is a perfect square? (a) 135 (b) 121 (c) 137
13. 13.A square garden has an area of 361 square m. How long is each side (in m)?
14. 14.What is √576? =
15. 15.What is the sum of the first 30 odd numbers (1 + 3 + 5 + …)?
16. 16.A square garden has an area of 2601 square m. How long is each side (in m)?
17. 17.What is √6889? =
18. 18.What is 19²? =
19. 19.What is the smallest whole number by which 325 must be divided to get a perfect square?
20. 20.A square garden has an area of 1681 square m. How long is each side (in m)?
21. 21.What is the smallest whole number by which 275 must be multiplied to get a perfect square?
22. 22.What is the sum of the first 20 odd numbers (1 + 3 + 5 + …)?
23. 23.Which of these is a perfect square? (a) 439 (b) 400 (c) 407
24. 24.What is the smallest whole number by which 360 must be divided to get a perfect square?
25. 25.What is the smallest whole number by which 343 must be divided to get a perfect square?
26. 26.What is the smallest whole number by which 294 must be divided to get a perfect square?
27. 27.What is 24²? =
28. 28.What is the smallest whole number by which 63 must be divided to get a perfect square?
29. 29.Which of these is a perfect square? (a) 273 (b) 256 (c) 286
30. 30.What is √4096? =
31. 31.What is the smallest whole number by which 160 must be divided to get a perfect square?
32. 32.What is the sum of the first 15 odd numbers (1 + 3 + 5 + …)?
33. 33.How many whole numbers lie between 44² and 45²?
34. 34.What is 64²? =
35. 35.What is 46²? =
36. 36.What is 18²? =
37. 37.What is the sum of the first 25 odd numbers (1 + 3 + 5 + …)?
38. 38.What is 29²? =
39. 39.What is 93²? =
40. 40.What is √256? =

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