Question

$$2 \sqrt{ 8 } +0.5 \sqrt{ 32 } - \frac{ 1 }{ 3 } \sqrt{ 18 }$$

Answer

5*sqrt(2)

Solution


Simplify  \(\sqrt{8}\)  to  \(2\sqrt{2}\).
\[2\times 2\sqrt{2}+0.5\sqrt{32}-\frac{1}{3}\sqrt{18}\]
Simplify  \(\sqrt{32}\)  to  \(4\sqrt{2}\).
\[2\times 2\sqrt{2}+0.5\times 4\sqrt{2}-\frac{1}{3}\sqrt{18}\]
Simplify  \(\sqrt{18}\)  to  \(3\sqrt{2}\).
\[2\times 2\sqrt{2}+0.5\times 4\sqrt{2}-\frac{1}{3}\times 3\sqrt{2}\]
Simplify  \(2\times 2\sqrt{2}\)  to  \(4\sqrt{2}\).
\[4\sqrt{2}+0.5\times 4\sqrt{2}-\frac{1}{3}\times 3\sqrt{2}\]
Simplify  \(0.5\times 4\sqrt{2}\)  to  \(2\sqrt{2}\).
\[4\sqrt{2}+2\sqrt{2}-\frac{1}{3}\times 3\sqrt{2}\]
Cancel \(3\).
\[4\sqrt{2}+2\sqrt{2}-\sqrt{2}\]
Simplify.
\[5\sqrt{2}\]

Decimal Form: 7.071068