Square Root

What Is the Square Root of -1? | Does -1 Have a Square Root?

Updated on: 12 Aug 2023

Contents

1. Square root of 0 2. Square root of 1 3. Square root of 2 4. Square root of 3 5. Square root of 4 6. Square root of 5 7. Square root of 6 8. Square root of 7 9. Square root of 8 10. Square root of 9 11. Square root of 10 12. Square root of 12 13. Square root of 13 14. Square root of 15 15. Square root of 16 16. Square root of 17 17. Square root of 18 18. Square root of 20 19. Square root of 24 20. Square root of 25 21. Square root of 27 22. Square root of 32 23. Square root of 34 24. Square root of 36 25. Square root of 40 26. Square root of 45 27. Square root of 49 28. Square root of 50 29. Square root of 64 30. Square root of 72 31. Square root of 75 32. Square root of 80 33. Square root of 81 34. Square root of 100 35. Square root of 121 36. Square root of 125 37. Square root of 144 38. Square root of 169 39. Square root of 196 40. Square root of 225 41. Square root of 256 42. Square root of 400 43. Square root of 900 44. Square root of 4761 45. Square root of pi

What Is the Square Root of -1? | Does -1 Have a Square Root?

The square root of -1 is i. The square root of any number has two possibilities which are a positive and a negative number. Let us take the number 36 as an example. The √36 = 6. The negative integer number or digit is not considered a square number and only the positive roots are used. That is because when we square or multiply those negative digits we again get a positive number.

That is (-6) (-6) = 36. Therefore the negative square of any number is considered imaginary and not a real value. This rule applies to -1. When we multiply (-1) (-1) we get 1. The thumb rule for finding the square root of any number is when you multiply a number twice it should give the original value but here we get 1 and not -1. Thus the imaginary roots of -1 are represented as i.

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Solved examples

Q1: Find the square root of -9
A1: √9 =√9 -1
Hence the square root of -9=3 i

Q2: Sonu has to find the square root of 36 using the long division method, help him

A2: √36 = 6

Q3: Find the square root of 1.
A3: The √1 = 1

Q4: Find the square root of -100.
A4: The √100 ×-1
√100 = 10
Hence, the √100 = 10i

Q5: What is the square root of 169?
A5:169 = 13 × 13
√169 = 13²
Hence, √169 = 13

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Frequently asked questions

What is the √-1
√-1 = i

Which method is used to find the -1
You can’t find the actual square root of the number as they have only imaginary roots and not real roots.

How to write the square root of 121 in exponential form?
121^1/2or 121^0.5is the exponential way to write √121

How to write the square root of 81 in radical form?
The radical form of writing square root is √81

What are the methods to find the square root of a number?
There are three methods to find the square root of a number
Prime factorization method
Long division method
Repeated subtraction

Written by

Prerit Jain

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