Answer:
B. √5
Step-by-step explanation:
Given:
[tex]K=\sqrt{9-4\sqrt{5}}[/tex]
[tex]\implies K+2=\sqrt{9-4\sqrt{5}}+2[/tex]
Rewrite 9 as 5 + 4:
[tex]= \sqrt{5-4\sqrt{5}+4}+2[/tex]
Rewrite 5 as (√5)², 4 as 2² and 4√5 as 2 · 2√5:
[tex]= \sqrt{(\sqrt{5})^2-2 \cdot 2\sqrt{5}+2^2}+2[/tex]
Apply the perfect square formula [tex]a^2-2ab+b^2=(a-b)^2[/tex]:
[tex]=\sqrt{(\sqrt{5}-2)^2}+2[/tex]
Apply radical rule [tex]\sqrt{a^2}=a[/tex]
[tex]=\sqrt{5}-2+2[/tex]
Simplify:
[tex]=\sqrt{5}[/tex]
