Question

$$5 \sqrt{ 8 } + \frac{ 1 }{ 2 } \sqrt{ 2 } -2 \sqrt{ 18 }$$

Answer

(9*sqrt(2))/2

Solution


Simplify  \(\sqrt{8}\)  to  \(2\sqrt{2}\).
\[5\times 2\sqrt{2}+\frac{1}{2}\sqrt{2}-2\sqrt{18}\]
Simplify  \(\sqrt{18}\)  to  \(3\sqrt{2}\).
\[5\times 2\sqrt{2}+\frac{1}{2}\sqrt{2}-2\times 3\sqrt{2}\]
Simplify  \(5\times 2\sqrt{2}\)  to  \(10\sqrt{2}\).
\[10\sqrt{2}+\frac{1}{2}\sqrt{2}-2\times 3\sqrt{2}\]
Simplify  \(\frac{1}{2}\sqrt{2}\)  to  \(\frac{\sqrt{2}}{2}\).
\[10\sqrt{2}+\frac{\sqrt{2}}{2}-2\times 3\sqrt{2}\]
Simplify  \(2\times 3\sqrt{2}\)  to  \(6\sqrt{2}\).
\[10\sqrt{2}+\frac{\sqrt{2}}{2}-6\sqrt{2}\]
Simplify.
\[\frac{9\sqrt{2}}{2}\]

Decimal Form: 6.363961