Question

The question is in the attached file

Answer 1

B. √5

Explanation:

Given:

`K=\sqrt{9-4√(5)}`

`\implies K+2=\sqrt{9-4√(5)}+2`

Rewrite 9 as 5 + 4:

`= \sqrt{5-4√(5)+4}+2`

Rewrite 5 as (√5)², 4 as 2² and 4√5 as 2 · 2√5:

`= \sqrt{(√(5))^2-2 \cdot 2√(5)+2^2}+2`

Apply the perfect square formula
`a^2-2ab+b^2=(a-b)^2`:

`=\sqrt{(√(5)-2)^2}+2`

Apply radical rule
`√(a^2)=a`

`=√(5)-2+2`

Simplify:

`=√(5)`