Question

$$4\sqrt{2}\cdot7\sqrt{32}$$

Answer

224

Solution


Simplify  \(\sqrt{32}\)  to  \(4\sqrt{2}\).
\[4\sqrt{2}\times 7\times 4\sqrt{2}\]
Simplify.
\[4\times 7\times 4\sqrt{2\times 2}\]
Simplify  \(2\times 2\)  to  \(4\).
\[4\times 7\times 4\sqrt{4}\]
Since \(2\times 2=4\), the square root of \(4\) is \(2\).
\[4\times 7\times 4\times 2\]
Simplify  \(4\times 7\)  to  \(28\).
\[28\times 4\times 2\]
Simplify  \(28\times 4\)  to  \(112\).
\[112\times 2\]
Simplify.
\[224\]