Solve (5sqrt{32})^2

$$( 5 \sqrt { 32 } ) ^ { 2 }$$

Evaluate

$$800$$

Solution Steps

Factor 32=4^{2}\times 2. Rewrite the square root of the product \sqrt{4^{2}\times 2} as the product of square roots \sqrt{4^{2}}\sqrt{2}. Take the square root of 4^{2}.

$$\left(5\times 4\sqrt{2}\right)^{2}$$

Multiply 5 and 4 to get 20.

$$\left(20\sqrt{2}\right)^{2}$$

Expand \left(20\sqrt{2}\right)^{2}.

$$20^{2}\left(\sqrt{2}\right)^{2}$$

Calculate 20 to the power of 2 and get 400.

$$400\left(\sqrt{2}\right)^{2}$$

The square of \sqrt{2} is 2.

$$400\times 2$$

Multiply 400 and 2 to get 800.

$$800$$

Factor

$$2^{5}\times 5^{2}$$