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

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

Evaluate

$$64\sqrt{2}\approx 90.509667992$$

Solution Steps

Calculate 8 to the power of 2 and get 64.

$$\sqrt{64\times \left(8\sqrt{2}\right)^{2}}$$

Expand \left(8\sqrt{2}\right)^{2}.

$$\sqrt{64\times 8^{2}\left(\sqrt{2}\right)^{2}}$$

Calculate 8 to the power of 2 and get 64.

$$\sqrt{64\times 64\left(\sqrt{2}\right)^{2}}$$

The square of \sqrt{2} is 2.

$$\sqrt{64\times 64\times 2}$$

Multiply 64 and 2 to get 128.

$$\sqrt{64\times 128}$$

Multiply 64 and 128 to get 8192.

$$\sqrt{8192}$$

Factor 8192=64^{2}\times 2. Rewrite the square root of the product \sqrt{64^{2}\times 2} as the product of square roots \sqrt{64^{2}}\sqrt{2}. Take the square root of 64^{2}.

$$64\sqrt{2}$$