Question

$$8+ \sqrt{ 2 \sqrt{ 7 \sqrt{ 9 } } } +$$

Answer

9+sqrt(2*sqrt(21))

Solution


Since \(3\times 3=9\), the square root of \(9\) is \(3\).
\[8+\sqrt{2\sqrt{7\times 3}}+\]
Simplify  \(7\times 3\)  to  \(21\).
\[8+\sqrt{2\sqrt{21}}+\]
Collect like terms.
\[8+\sqrt{2\sqrt{21}}+1\]
Collect like terms.
\[(8+1)+\sqrt{2\sqrt{21}}\]
Simplify.
\[9+\sqrt{2\sqrt{21}}\]

Decimal Form: 12.027400