Question

Refer to attachment for question

Answer 1

Answer:

Below!

Step-by-step explanation:

Let the irrational number be known as "x".

$\implies -\sqrt{41} \times x = 1$

Divide both sides by -√41.

$\implies \dfrac{(-\sqrt{41} \times x)}{-\sqrt{41} } = \dfrac{1}{\sqrt{-41} }$

$\implies x = \dfrac{1}{-\sqrt{41} }$

Take the "-" to the numerator:

$\implies x = \dfrac{-1}{\sqrt{41} }$

Use parenthesis to isolate the "-"

$\implies x = -\huge\text{(}\dfrac{1}{\sqrt{41} } \huge\text{)}$

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

$\implies {x = -\huge\text{(}\dfrac{\sqrt{1}}{\sqrt{41} }\huge\text{)}}$

Combine the roots in the equation:

$\implies {x = -\huge\text{(}\sqrt{\dfrac{1}{41} }} \huge\text{)}}$

Remove the parenthesis:

$\implies {x = -\sqrt{\dfrac{1}{41} }}$

Thus, Option C is correct.