Chapter 7.4, Problem 48PPS

To determine

To simplify the expression $\frac{3}{\sqrt{7}-\sqrt{2}}$ .

Answer to Problem 48PPS

  $\frac{3}{5}(\sqrt{7}+\sqrt{2})$

Explanation of Solution

Given:

  $\frac{3}{\sqrt{7}-\sqrt{2}}$

Formula used:

  $(a+b)(a-b)=a^2-b^2$

Calculation:

  $\begin{array}{l}\Rightarrow \frac{3}{\sqrt{7}-\sqrt{2}}\\ \Rightarrow \frac{3}{\sqrt{7}-\sqrt{2}}\times \frac{\sqrt{7}+\sqrt{2}}{\sqrt{7}+\sqrt{2}}[\because \text{Rationalizing the denominator}]\\ \Rightarrow \frac{3(\sqrt{7}+\sqrt{2})}{(\sqrt{7}-\sqrt{2})(\sqrt{7}+\sqrt{2})}\\ \Rightarrow \frac{3(\sqrt{7}+\sqrt{2})}{{(\sqrt{7})}^2-{(\sqrt{2})}^2}[\because (a+b)(a-b)=a^2-b^2]\\ \Rightarrow \frac{3(\sqrt{7}+\sqrt{2})}{7-2}\\ \Rightarrow \frac{3}{5}(\sqrt{7}+\sqrt{2})\end{array}$

Conclusion:

The simplified form of the given expression is equal to $\frac{3}{5}(\sqrt{7}+\sqrt{2})$ .