Question

Refer to attachment for question

Answer 1

Below!

Explanation:

Let the irrational number be known as "x".

`\implies -√(41) * x = 1`

Divide both sides by -√41.

`\implies ((-√(41) * x))/(-√(41) ) = (1)/(√(-41) )`

`\implies x = (1)/(-√(41) )`

Take the "-" to the numerator:

`\implies x = (-1)/(√(41) )`

Use parenthesis to isolate the "-"

`\implies x = -\huge\text{(}(1)/(√(41) ) \huge\text{)}`

Note: 1 can also be written as √1. (√1 = √1 × √1 = 1)

`\implies {x = -\huge\text{(}(√(1))/(√(41) )\huge\text{)}}`

Combine the roots in the equation:

`\implies {x = -\huge\text{(}\sqrt{(1)/(41) }} \huge\text{)}}`

Remove the parenthesis:

`\implies {x = -\sqrt{(1)/(41) }}`

Thus, Option C is correct.