Solve 2:sqrt{7}-sqrt{54}

$$2 : \sqrt { 7 } - \sqrt { 54 }$$

Evaluate

$$\frac{2\sqrt{7}}{7}-3\sqrt{6}\approx -6.592540282$$

Short Solution Steps

Rationalize the denominator of \frac{2}{\sqrt{7}} by multiplying numerator and denominator by \sqrt{7}.

$$\frac{2\sqrt{7}}{\left(\sqrt{7}\right)^{2}}-\sqrt{54}$$

The square of \sqrt{7} is 7.

$$\frac{2\sqrt{7}}{7}-\sqrt{54}$$

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}.

$$\frac{2\sqrt{7}}{7}-3\sqrt{6}$$

To add or subtract expressions, expand them to make their denominators the same. Multiply -3\sqrt{6} times \frac{7}{7}.

$$\frac{2\sqrt{7}}{7}+\frac{7\left(-3\right)\sqrt{6}}{7}$$

Since \frac{2\sqrt{7}}{7} and \frac{7\left(-3\right)\sqrt{6}}{7} have the same denominator, add them by adding their numerators.

$$\frac{2\sqrt{7}+7\left(-3\right)\sqrt{6}}{7}$$

Do the multiplications in 2\sqrt{7}+7\left(-3\right)\sqrt{6}.

$$\frac{2\sqrt{7}-21\sqrt{6}}{7}$$