Chapter 6.4, Problem 15WE

To determine

To Simplify:

  $\left(\sqrt{11}-\sqrt{7}\right)\left(\sqrt{11}+\sqrt{7}\right)$

Answer to Problem 15WE

4

Explanation of Solution

Given:

The expression is :

  $\left(\sqrt{11}-\sqrt{7}\right)\left(\sqrt{11}+\sqrt{7}\right)$

Formula Used:

  $\left(a+b\right)\left(a-b\right)=a^2-b^2$

Calculation:

Given:

  $\left(\sqrt{11}-\sqrt{7}\right)\left(\sqrt{11}+\sqrt{7}\right)\mathrm{.........}(1)$

Use

  $\left(a+b\right)\left(a-b\right)=a^2-b^2\mathrm{.........}(2)$

Comparing equation (1) with (2),

  $a=\sqrt{11},b=\sqrt{7}$

Substitute the values in equation (2),

  $\begin{array}{l}\left(a+b\right)\left(a-b\right)=a^2-b^2\\ \Rightarrow \left(\sqrt{11}-\sqrt{7}\right)\left(\sqrt{11}+\sqrt{7}\right)={\left(\sqrt{11}\right)}^2-{\left(\sqrt{7}\right)}^2=11-7=4\end{array}$