What is the simplified value of $$\frac{\sqrt{9}+\sqrt{7}}{\sqrt{9}-\sqrt{7}}$$ ?
Expression : $$\frac{\sqrt{9}+\sqrt{7}}{\sqrt{9}-\sqrt{7}}$$
Rationalizing the denominator, we get :
=Â $$\frac{\sqrt{9}+\sqrt{7}}{\sqrt{9}-\sqrt{7}}\times(\frac{\sqrt9+\sqrt7}{\sqrt9+\sqrt7})$$
= $$\frac{(\sqrt9+\sqrt7)^2}{(\sqrt9-\sqrt7)(\sqrt9+\sqrt7)}$$
= $$\frac{9+7+2(\sqrt9)(\sqrt7)}{9-7}$$
= $$\frac{16+2\sqrt{63}}{2}$$
= $$8+\sqrt{63}=8+3\sqrt7$$
=> Ans - (A)
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