Solve sqrt{75}-2/sqrt{3}

$$\sqrt { 75 } - \frac { 2 } { \sqrt { 3 } }$$

Evaluate

$$\frac{13\sqrt{3}}{3}\approx 7.505553499$$

Solution Steps

Factor 75=5^{2}\times 3. Rewrite the square root of the product \sqrt{5^{2}\times 3} as the product of square roots \sqrt{5^{2}}\sqrt{3}. Take the square root of 5^{2}.

$$5\sqrt{3}-\frac{2}{\sqrt{3}}$$

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

$$5\sqrt{3}-\frac{2\sqrt{3}}{\left(\sqrt{3}\right)^{2}}$$

The square of \sqrt{3} is 3.

$$5\sqrt{3}-\frac{2\sqrt{3}}{3}$$

Combine 5\sqrt{3} and -\frac{2\sqrt{3}}{3} to get \frac{13}{3}\sqrt{3}.

$$\frac{13}{3}\sqrt{3}$$