Solve 15/sqrt{3}-sqrt{27}

$$\frac { 15 } { \sqrt { 3 } } - \sqrt { 27 }$$

Evaluate

$$2\sqrt{3}\approx 3.464101615$$

Solution Steps

Rationalize the denominator of \frac{15}{\sqrt{3}} by multiplying numerator and denominator by \sqrt{3}.

$$\frac{15\sqrt{3}}{\left(\sqrt{3}\right)^{2}}-\sqrt{27}$$

The square of \sqrt{3} is 3.

$$\frac{15\sqrt{3}}{3}-\sqrt{27}$$

Divide 15\sqrt{3} by 3 to get 5\sqrt{3}.

$$5\sqrt{3}-\sqrt{27}$$

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}.

$$5\sqrt{3}-3\sqrt{3}$$

Combine 5\sqrt{3} and -3\sqrt{3} to get 2\sqrt{3}.

$$2\sqrt{3}$$