Question

$$3 \sqrt{ 48 } - \sqrt{ 75 } + \frac{ 1 }{ 7 } \sqrt{ 147 }$$

Answer

8*sqrt(3)

Solution


Simplify  \(\sqrt{48}\)  to  \(4\sqrt{3}\).
\[3\times 4\sqrt{3}-\sqrt{75}+\frac{1}{7}\sqrt{147}\]
Simplify  \(\sqrt{75}\)  to  \(5\sqrt{3}\).
\[3\times 4\sqrt{3}-5\sqrt{3}+\frac{1}{7}\sqrt{147}\]
Simplify  \(\sqrt{147}\)  to  \(7\sqrt{3}\).
\[3\times 4\sqrt{3}-5\sqrt{3}+\frac{1}{7}\times 7\sqrt{3}\]
Simplify  \(3\times 4\sqrt{3}\)  to  \(12\sqrt{3}\).
\[12\sqrt{3}-5\sqrt{3}+\frac{1}{7}\times 7\sqrt{3}\]
Cancel \(7\).
\[12\sqrt{3}-5\sqrt{3}+\sqrt{3}\]
Simplify.
\[8\sqrt{3}\]

Decimal Form: 13.856406