Class 8 Maths Worksheet: Squares and Square Roots

Maths worksheets lesson 58: Squares and square roots · Set 439 · 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 √256? =
2. 2.A square garden has an area of 676 square m. How long is each side (in m)?
3. 3.A square garden has an area of 2209 square m. How long is each side (in m)?
4. 4.What is the sum of the first 21 odd numbers (1 + 3 + 5 + …)?
5. 5.How many whole numbers lie between 44² and 45²?
6. 6.A square garden has an area of 2916 square m. How long is each side (in m)?
7. 7.What is 80²? =
8. 8.Which of these is a perfect square? (a) 737 (b) 758 (c) 729
9. 9.What is 63²? =
10. 10.What is the smallest whole number by which 50 must be multiplied to get a perfect square?
11. 11.Which of these is a perfect square? (a) 1587 (b) 1559 (c) 1521
12. 12.What is 43²? =
13. 13.Which of these is a perfect square? (a) 130 (b) 142 (c) 121
14. 14.What is the smallest whole number by which 147 must be multiplied to get a perfect square?
15. 15.What is 18²? =
16. 16.What is the smallest whole number by which 44 must be multiplied to get a perfect square?
17. 17.What is 26²? =
18. 18.What is √6084? =
19. 19.What is the smallest whole number by which 567 must be multiplied to get a perfect square?
20. 20.What is the smallest whole number by which 891 must be multiplied to get a perfect square?
21. 21.What is the sum of the first 10 odd numbers (1 + 3 + 5 + …)?
22. 22.What is √676? =
23. 23.What is 23²? =
24. 24.What is the sum of the first 7 odd numbers (1 + 3 + 5 + …)?
25. 25.What is √7744? =
26. 26.What is √9216? =
27. 27.What is the sum of the first 20 odd numbers (1 + 3 + 5 + …)?
28. 28.A square garden has an area of 361 square m. How long is each side (in m)?
29. 29.How many whole numbers lie between 23² and 24²?
30. 30.How many whole numbers lie between 21² and 22²?
31. 31.What is the smallest whole number by which 45 must be multiplied to get a perfect square?
32. 32.What is √196? =
33. 33.What is 42²? =
34. 34.What is the smallest whole number by which 240 must be multiplied to get a perfect square?
35. 35.What is the smallest whole number by which 891 must be divided to get a perfect square?
36. 36.What is √361? =
37. 37.What is the smallest whole number by which 896 must be multiplied to get a perfect square?
38. 38.What is the sum of the first 15 odd numbers (1 + 3 + 5 + …)?
39. 39.Which of these is a perfect square? (a) 400 (b) 438 (c) 401
40. 40.A square garden has an area of 2116 square m. How long is each side (in m)?

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