Question

$$\sqrt{ 13 \times 3 \times 2 \times 13 \times 2 \times 13 \times 7 \times 7 }$$

Answer

182*sqrt(39)

Solution


Simplify  \(13\times 3\)  to  \(39\).
\[\sqrt{39\times 2\times 13\times 2\times 13\times 7\times 7}\]
Simplify  \(39\times 2\)  to  \(78\).
\[\sqrt{78\times 13\times 2\times 13\times 7\times 7}\]
Simplify  \(78\times 13\)  to  \(1014\).
\[\sqrt{1014\times 2\times 13\times 7\times 7}\]
Simplify  \(1014\times 2\)  to  \(2028\).
\[\sqrt{2028\times 13\times 7\times 7}\]
Simplify  \(2028\times 13\)  to  \(26364\).
\[\sqrt{26364\times 7\times 7}\]
Simplify  \(26364\times 7\)  to  \(184548\).
\[\sqrt{184548\times 7}\]
Simplify  \(184548\times 7\)  to  \(1291836\).
\[\sqrt{1291836}\]
Simplify  \(\sqrt{1291836}\)  to  \(182\sqrt{39}\).
\[182\sqrt{39}\]

Decimal Form: 1136.589636