Question

$$3\sqrt{108-3\sqrt{48}-\sqrt{75}$$

Answer

sqrt(3)

Solution


Simplify  \(\sqrt{108}\)  to  \(6\sqrt{3}\).
\[3\times 6\sqrt{3}-3\sqrt{48}-\sqrt{75}\]
Simplify  \(\sqrt{48}\)  to  \(4\sqrt{3}\).
\[3\times 6\sqrt{3}-3\times 4\sqrt{3}-\sqrt{75}\]
Simplify  \(\sqrt{75}\)  to  \(5\sqrt{3}\).
\[3\times 6\sqrt{3}-3\times 4\sqrt{3}-5\sqrt{3}\]
Simplify  \(3\times 6\sqrt{3}\)  to  \(18\sqrt{3}\).
\[18\sqrt{3}-3\times 4\sqrt{3}-5\sqrt{3}\]
Simplify  \(3\times 4\sqrt{3}\)  to  \(12\sqrt{3}\).
\[18\sqrt{3}-12\sqrt{3}-5\sqrt{3}\]
Simplify.
\[\sqrt{3}\]

Decimal Form: 1.732051