Question

please help me to solve this

Answer 1

IO THINK THE ANSWER IS 2. BY USING CONJUCATE METHOD WE GET THE ANSWER IN THE OPTION 2.

Answer 2

Answer:

(2)√5 + 2

Step-by-step explanation:

To find:

$\sqrt{\frac{\sqrt{5} +2}{\sqrt{5} -2}$

Let us first solve

$\frac{\sqrt{5}+2}{\sqrt{5}-2}$

To remove the irrational number from the denominator, we multiply the numerator and denominator by (√5 + 2)

$\frac{\sqrt{5}+2}{\sqrt{5}-2} = \frac{\sqrt{5}+2}{\sqrt{5}-2} * frac{\sqrt{5}+2}{\sqrt{5}+2}\\ \\ = \frac{(\sqrt{5}+2)^{2}}{5-4} = (\sqrt{5}+2)^{2}$

Now,

$\sqrt{\frac{\sqrt{5} +2}{\sqrt{5} -2}=\sqrt{(\sqrt{5}+2)^{2}}=\sqrt{5}+2$

∴ (2) √5 + 2 is the answer