Question 11

$$\sqrt{3+\sqrt{5}}=$$

Solution

Let , $$\sqrt{3+\sqrt{5}}=X$$

So, $$X^2=3+\sqrt{5}$$
= $$\ \dfrac{\ 5}{2}+\dfrac{\ 1}{2}+\sqrt{5}$$
= $$\ \dfrac{\ 5}{2}+\dfrac{\ 1}{2}+2\ \left(\dfrac{\ \sqrt{5}}{\sqrt{2}\times\sqrt{2}}\right)$$

= $$\left(\sqrt{\dfrac{5}{2}}+\sqrt{\dfrac{1}{2}}\right)^2$$

Therefore, X = $$\sqrt{\dfrac{5}{2}}+\sqrt{\dfrac{1}{2}}$$

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