Solve (sqrt{18}-24)divsqrt{6}

$$( \sqrt { 18 } - 24 ) \div \sqrt { 6 }$$

Evaluate

$$\sqrt{3}-4\sqrt{6}\approx -8.065908164$$

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}.

$$\frac{3\sqrt{2}-24}{\sqrt{6}}$$

Rationalize the denominator of \frac{3\sqrt{2}-24}{\sqrt{6}} by multiplying numerator and denominator by \sqrt{6}.

$$\frac{\left(3\sqrt{2}-24\right)\sqrt{6}}{\left(\sqrt{6}\right)^{2}}$$

The square of \sqrt{6} is 6.

$$\frac{\left(3\sqrt{2}-24\right)\sqrt{6}}{6}$$

Use the distributive property to multiply 3\sqrt{2}-24 by \sqrt{6}.

$$\frac{3\sqrt{2}\sqrt{6}-24\sqrt{6}}{6}$$

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}.

$$\frac{3\sqrt{2}\sqrt{2}\sqrt{3}-24\sqrt{6}}{6}$$

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

$$\frac{3\times 2\sqrt{3}-24\sqrt{6}}{6}$$

Multiply 3 and 2 to get 6.

$$\frac{6\sqrt{3}-24\sqrt{6}}{6}$$

Divide each term of 6\sqrt{3}-24\sqrt{6} by 6 to get \sqrt{3}-4\sqrt{6}.

$$\sqrt{3}-4\sqrt{6}$$