Question

$$A=\sqrt{9+\sqrt{80}-9\sqrt{9-\sqrt{80}}$$

Answer

A=-24

Solution


Since \(3\times 3=9\), the square root of \(9\) is \(3\).
\[A=3+\sqrt{80}-9\times 3-\sqrt{80}\]
Simplify  \(\sqrt{80}\)  to  \(4\sqrt{5}\).
\[A=3+4\sqrt{5}-9\times 3-4\sqrt{5}\]
Simplify  \(9\times 3\)  to  \(27\).
\[A=3+4\sqrt{5}-27-4\sqrt{5}\]
Simplify  \(3+4\sqrt{5}-27-4\sqrt{5}\)  to  \(-24\).
\[A=-24\]