Solve sqrt{2}*sqrt{8}sqrt[3]{-27}

$$\sqrt{ 2 } \times \sqrt{ 8 } \sqrt[3]{ -27 }$$

Evaluate

$$-12$$

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}.

$$\sqrt{2}\sqrt{2}\sqrt{4}\sqrt[3]{-27}$$

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

$$2\sqrt{4}\sqrt[3]{-27}$$

Calculate the square root of 4 and get 2.

$$2\times 2\sqrt[3]{-27}$$

Multiply 2 and 2 to get 4.

$$4\sqrt[3]{-27}$$

Calculate \sqrt[3]{-27} and get -3.

$$4\left(-3\right)$$

Multiply 4 and -3 to get -12.

$$-12$$

Factor

$$-12$$