Solve 2sqrt{2}*4sqrt{8}

$$2 \sqrt { 2 } \cdot 4 \sqrt { 8 }$$

Evaluate

$$32$$

Solution Steps

Factor 8=2\times 4. Rewrite the square root of the product \sqrt{2\times 4} as the product of square roots \sqrt{2}\sqrt{4}.

$$2\times 4\sqrt{2}\sqrt{2}\sqrt{4}$$

Multiply \sqrt{2} and \sqrt{2} to get 2.

$$2\times 4\times 2\sqrt{4}$$

Multiply 2 and 4 to get 8.

$$8\times 2\sqrt{4}$$

Multiply 8 and 2 to get 16.

$$16\sqrt{4}$$

Calculate the square root of 4 and get 2.

$$16\times 2$$

Multiply 16 and 2 to get 32.

$$32$$

Factor

$$2^{5}$$