Question

Write two expressions equivalent to `sqrt -49` . how can you do this?

`sqrt -49`

Answer 1

`sqrt(-49)=sqrt49xxsqrt(-1)=+-7i` i.e. `7i` and `-7i`

Explanation:

Well if you need square root of a negative number, you have to move to the domain of complex numbers.

In complex number we use a number `i`, which is defined so that `i^2=-1` i.e. `sqrt(-1)=i`.

Hence `sqrt(-49)=sqrt(49xx(-1))=sqrt49xxsqrt(-1)`

and as we can have both `7` and `-7` as `sqrt49`

`sqrt(-49)=sqrt49xxsqrt(-1)=+-7i` i.e. `7i` and `-7i`