Solve 2sqrt{3}*3sqrt{27}

$$2 \sqrt { 3 } \cdot 3 \sqrt { 27 }$$

Evaluate

$$54$$

Solution Steps

Factor 27=3\times 9. Rewrite the square root of the product \sqrt{3\times 9} as the product of square roots \sqrt{3}\sqrt{9}.

$$2\times 3\sqrt{3}\sqrt{3}\sqrt{9}$$

Multiply \sqrt{3} and \sqrt{3} to get 3.

$$2\times 3\times 3\sqrt{9}$$

Multiply 2 and 3 to get 6.

$$6\times 3\sqrt{9}$$

Multiply 6 and 3 to get 18.

$$18\sqrt{9}$$

Calculate the square root of 9 and get 3.

$$18\times 3$$

Multiply 18 and 3 to get 54.

$$54$$

Factor

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