Solve 3sqrt{3}(sqrt{18}-sqrt{2})divsqrt{3}

$$3 \sqrt { 3 } ( \sqrt { 18 } - \sqrt { 2 } ) \div \sqrt { 3 }$$

Evaluate

$$6\sqrt{2}\approx 8.485281374$$

Solution Steps

Factor 18=3^{2}\times 2. Rewrite the square root of the product \sqrt{3^{2}\times 2} as the product of square roots \sqrt{3^{2}}\sqrt{2}. Take the square root of 3^{2}.

$$\frac{3\sqrt{3}\left(3\sqrt{2}-\sqrt{2}\right)}{\sqrt{3}}$$

Combine 3\sqrt{2} and -\sqrt{2} to get 2\sqrt{2}.

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

Multiply 3 and 2 to get 6.

$$\frac{6\sqrt{3}\sqrt{2}}{\sqrt{3}}$$

To multiply \sqrt{3} and \sqrt{2}, multiply the numbers under the square root.

$$\frac{6\sqrt{6}}{\sqrt{3}}$$

Rationalize the denominator of \frac{6\sqrt{6}}{\sqrt{3}} by multiplying numerator and denominator by \sqrt{3}.

$$\frac{6\sqrt{6}\sqrt{3}}{\left(\sqrt{3}\right)^{2}}$$

The square of \sqrt{3} is 3.

$$\frac{6\sqrt{6}\sqrt{3}}{3}$$

Factor 6=3\times 2. Rewrite the square root of the product \sqrt{3\times 2} as the product of square roots \sqrt{3}\sqrt{2}.

$$\frac{6\sqrt{3}\sqrt{2}\sqrt{3}}{3}$$

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

$$\frac{6\times 3\sqrt{2}}{3}$$

Cancel out 3 and 3.

$$6\sqrt{2}$$