Solve (2sqrt{18}-sqrt{12})divsqrt{6}

$$(2 \sqrt{ 18 } - \sqrt{ 12 } ) \div \sqrt{ 6 }$$

Evaluate

$$\sqrt{2}\left(\sqrt{6}-1\right)\approx 2.049888053$$

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}.

$$\frac{2\times 3\sqrt{2}-\sqrt{12}}{\sqrt{6}}$$

Multiply 2 and 3 to get 6.

$$\frac{6\sqrt{2}-\sqrt{12}}{\sqrt{6}}$$

Factor 12=2^{2}\times 3. Rewrite the square root of the product \sqrt{2^{2}\times 3} as the product of square roots \sqrt{2^{2}}\sqrt{3}. Take the square root of 2^{2}.

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

Rationalize the denominator of \frac{6\sqrt{2}-2\sqrt{3}}{\sqrt{6}} by multiplying numerator and denominator by \sqrt{6}.

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

The square of \sqrt{6} is 6.

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

Use the distributive property to multiply 6\sqrt{2}-2\sqrt{3} by \sqrt{6}.

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

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

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

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

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

Multiply 6 and 2 to get 12.

$$\frac{12\sqrt{3}-2\sqrt{3}\sqrt{6}}{6}$$

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}.

$$\frac{12\sqrt{3}-2\sqrt{3}\sqrt{3}\sqrt{2}}{6}$$

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

$$\frac{12\sqrt{3}-2\times 3\sqrt{2}}{6}$$

Multiply -2 and 3 to get -6.

$$\frac{12\sqrt{3}-6\sqrt{2}}{6}$$

Divide each term of 12\sqrt{3}-6\sqrt{2} by 6 to get 2\sqrt{3}-\sqrt{2}.

$$2\sqrt{3}-\sqrt{2}$$