Solve {left(78sqrt{56}right)}^2=

$${ \left(78 \sqrt{ 56 } \right) }^{ 2 } =$$

Evaluate

$$340704$$

Solution Steps

Factor 56=2^{2}\times 14. Rewrite the square root of the product \sqrt{2^{2}\times 14} as the product of square roots \sqrt{2^{2}}\sqrt{14}. Take the square root of 2^{2}.

$$\left(78\times 2\sqrt{14}\right)^{2}$$

Multiply 78 and 2 to get 156.

$$\left(156\sqrt{14}\right)^{2}$$

Expand \left(156\sqrt{14}\right)^{2}.

$$156^{2}\left(\sqrt{14}\right)^{2}$$

Calculate 156 to the power of 2 and get 24336.

$$24336\left(\sqrt{14}\right)^{2}$$

The square of \sqrt{14} is 14.

$$24336\times 14$$

Multiply 24336 and 14 to get 340704.

$$340704$$

Factor

$$2^{5}\times 3^{2}\times 7\times 13^{2}$$