Solve frac{2xsqrt{36}}{xsqrt{27}}

$$\frac { 2 x \sqrt { 36 } } { x \sqrt { 27 } }$$

Evaluate

$$\frac{4\sqrt{3}}{3}\approx 2.309401077$$

Solution Steps

Cancel out x in both numerator and denominator.

$$\frac{2\sqrt{36}}{\sqrt{27}}$$

Calculate the square root of 36 and get 6.

$$\frac{2\times 6}{\sqrt{27}}$$

Multiply 2 and 6 to get 12.

$$\frac{12}{\sqrt{27}}$$

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}.

$$\frac{12}{3\sqrt{3}}$$

Rationalize the denominator of \frac{12}{3\sqrt{3}} by multiplying numerator and denominator by \sqrt{3}.

$$\frac{12\sqrt{3}}{3\left(\sqrt{3}\right)^{2}}$$

The square of \sqrt{3} is 3.

$$\frac{12\sqrt{3}}{3\times 3}$$

Cancel out 3 in both numerator and denominator.

$$\frac{4\sqrt{3}}{3}$$