Question 52

What is the simplified value of $$\frac{\sqrt{9}+\sqrt{7}}{\sqrt{9}-\sqrt{7}}$$ ?

Solution

Expression : $$\frac{\sqrt{9}+\sqrt{7}}{\sqrt{9}-\sqrt{7}}$$

Rationalizing the denominator, we get :

= $$\frac{\sqrt{9}+\sqrt{7}}{\sqrt{9}-\sqrt{7}}\times(\frac{\sqrt9+\sqrt7}{\sqrt9+\sqrt7})$$

= $$\frac{(\sqrt9+\sqrt7)^2}{(\sqrt9-\sqrt7)(\sqrt9+\sqrt7)}$$

= $$\frac{9+7+2(\sqrt9)(\sqrt7)}{9-7}$$

= $$\frac{16+2\sqrt{63}}{2}$$

= $$8+\sqrt{63}=8+3\sqrt7$$

=> Ans - (A)

Share on Whatsapp Share on Whatsapp

Create a FREE account and get: