Solve -sqrt{2}divsqrt{54}

$$- \sqrt{ 2 } \div \sqrt{ 54 }$$

Evaluate

$$-\frac{\sqrt{3}}{9}\approx -0.19245009$$

Solution Steps

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}.

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

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

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

The square of \sqrt{6} is 6.

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

Multiply 3 and 6 to get 18.

$$\frac{\left(-\sqrt{2}\right)\sqrt{6}}{18}$$

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}.

$$\frac{-\sqrt{2}\sqrt{2}\sqrt{3}}{18}$$

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

$$\frac{-2\sqrt{3}}{18}$$

Divide -2\sqrt{3} by 18 to get -\frac{1}{9}\sqrt{3}.

$$-\frac{1}{9}\sqrt{3}$$