Question

Which of the following is the value of $\left(\sqrt{11}-\sqrt{7}\right)\left(\sqrt{11}+\sqrt{7}\right)$?
(a) –4
(b) 4
(c) $\sqrt{11}$
(d) $\sqrt{7}$

Answer 1

$$\begin{gathered} \left(\sqrt{11}-\sqrt{7}\right)\left(\sqrt{11}+\sqrt{7}\right) \\ ={\left(\sqrt{11}\right)}^2-{\left(\sqrt{7}\right)}^2\left[\left(a-b\right)\left(a+b\right)=a^2-b^2\right] \\ =11-7 \\ =4 \end{gathered}$$
Hence, the correct answer is option (b).