Solve frac{sqrt{18}}{sqrt{27}}*2

$$\frac{ \sqrt{ 18 } }{ \sqrt{ 27 } } \times 2$$

Evaluate

$$\frac{2\sqrt{6}}{3}\approx 1.632993162$$

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}.

$$2\times \frac{3\sqrt{2}}{\sqrt{27}}$$

Factor 27=3^{2}\times 3. Rewrite the square root of the product \sqrt{3^{2}\times 3} as the product of square roots \sqrt{3^{2}}\sqrt{3}. Take the square root of 3^{2}.

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

Cancel out 3 in both numerator and denominator.

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

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

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

The square of \sqrt{3} is 3.

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

To multiply \sqrt{2} and \sqrt{3}, multiply the numbers under the square root.

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

Express 2\times \frac{\sqrt{6}}{3} as a single fraction.

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