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

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

Evaluate

$$5$$

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 5\sqrt{3}.

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

Rationalize the denominator of \frac{5\sqrt{3}}{\sqrt{3}} by multiplying numerator and denominator by \sqrt{3}.

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

The square of \sqrt{3} is 3.

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

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

$$\frac{5\times 3}{3}$$

Multiply 5 and 3 to get 15.

$$\frac{15}{3}$$

Divide 15 by 3 to get 5.

$$5$$

Factor

$$5$$