Solve frac{sqrt{27}-sqrt{12}}{sqrt{3}}

$$\frac { \sqrt { 27 } - \sqrt { 12 } } { \sqrt { 3 } }$$

Evaluate

$$1$$

Solution Steps

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}.

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

Factor 12=2^{2}\times 3. Rewrite the square root of the product \sqrt{2^{2}\times 3} as the product of square roots \sqrt{2^{2}}\sqrt{3}. Take the square root of 2^{2}.

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

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

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

Rewrite the division of square roots \frac{\sqrt{3}}{\sqrt{3}} as the square root of the division \sqrt{\frac{3}{3}} and perform the division.

$$\sqrt{1}$$

Calculate the square root of 1 and get 1.

$$1$$

Factor

$$1$$