Question

Which of the following is equivalent to

Answer 1

Choice B is correct.

Explanation:

Given expression is

18-√-25

We have to simplify it.

As we know that

√-a=√-1.√a

Since we know that √-1=i

Hence,√-a=√ai

we can simplify given expression by using above equation.

18-√-25

18-√-1√25

18-i√25

18-√25i

As 25 is square of 5.

Hence ,

18-5i which is the answer.

Answer 2

Option (2) is correct.

`18-√(-25)=18-5i`

Explanation:

Given expression
`18-√(-25)`

We have to find an equivalence value to the expression.

Radical rule,

`√(-a)=√(-1) √(a)`

Also,
`i=√(-1)`

Consider the given expression,

`18-√(-25)`

Applying radical rule to
`√(-25)`

`√(-25)=√(-1)√(25)=5i`

Thus, the expression becomes,

`18-√(-25)=18-5i`

Thus, option (2) is correct.