Solve (sqrt{24}-sqrt{54}):sqrt{6}

$$( \sqrt { 24 } - \sqrt { 54 } ) : \sqrt { 6 }$$

Evaluate

$$-1$$

Solution Steps

Factor 24=2^{2}\times 6. Rewrite the square root of the product \sqrt{2^{2}\times 6} as the product of square roots \sqrt{2^{2}}\sqrt{6}. Take the square root of 2^{2}.

$$\frac{2\sqrt{6}-\sqrt{54}}{\sqrt{6}}$$

Factor 54=3^{2}\times 6. Rewrite the square root of the product \sqrt{3^{2}\times 6} as the product of square roots \sqrt{3^{2}}\sqrt{6}. Take the square root of 3^{2}.

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

Combine 2\sqrt{6} and -3\sqrt{6} to get -\sqrt{6}.

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

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

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

The square of \sqrt{6} is 6.

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

Multiply \sqrt{6} and \sqrt{6} to get 6.

$$\frac{-6}{6}$$

Divide -6 by 6 to get -1.

$$-1$$

Factor

$$-1$$