Solve {left(7sqrt{8}right)}^2

$${ \left(7 \sqrt{ 8 } \right) }^{ 2 }$$

Evaluate

$$392$$

Solution Steps

Factor 8=2^{2}\times 2. Rewrite the square root of the product \sqrt{2^{2}\times 2} as the product of square roots \sqrt{2^{2}}\sqrt{2}. Take the square root of 2^{2}.

$$\left(7\times 2\sqrt{2}\right)^{2}$$

Multiply 7 and 2 to get 14.

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

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

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

Calculate 14 to the power of 2 and get 196.

$$196\left(\sqrt{2}\right)^{2}$$

The square of \sqrt{2} is 2.

$$196\times 2$$

Multiply 196 and 2 to get 392.

$$392$$

Factor

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