Solve (sqrt{12}-sqrt{27})divsqrt{3}

$$( \sqrt{ 12 } - \sqrt{ 27 } ) \div \sqrt{ 3 }$$

Evaluate

$$-1$$

Solution Steps

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}.

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

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}.

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

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

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

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

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

The square of \sqrt{3} is 3.

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

Multiply \sqrt{3} and \sqrt{3} to get 3.

$$\frac{-3}{3}$$

Divide -3 by 3 to get -1.

$$-1$$

Factor

$$-1$$