Solve 2sqrt{12}+4sqrt{18}divsqrt{3}

$$2 \sqrt{ 12 } +4 \sqrt{ 18 } \div \sqrt{ 3 }$$

Evaluate

$$4\left(\sqrt{3}+\sqrt{6}\right)\approx 16.726162201$$

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}.

$$2\times 2\sqrt{3}+\frac{4\sqrt{18}}{\sqrt{3}}$$

Multiply 2 and 2 to get 4.

$$4\sqrt{3}+\frac{4\sqrt{18}}{\sqrt{3}}$$

Factor 18=3^{2}\times 2. Rewrite the square root of the product \sqrt{3^{2}\times 2} as the product of square roots \sqrt{3^{2}}\sqrt{2}. Take the square root of 3^{2}.

$$4\sqrt{3}+\frac{4\times 3\sqrt{2}}{\sqrt{3}}$$

Multiply 4 and 3 to get 12.

$$4\sqrt{3}+\frac{12\sqrt{2}}{\sqrt{3}}$$

Rationalize the denominator of \frac{12\sqrt{2}}{\sqrt{3}} by multiplying numerator and denominator by \sqrt{3}.

$$4\sqrt{3}+\frac{12\sqrt{2}\sqrt{3}}{\left(\sqrt{3}\right)^{2}}$$

The square of \sqrt{3} is 3.

$$4\sqrt{3}+\frac{12\sqrt{2}\sqrt{3}}{3}$$

To multiply \sqrt{2} and \sqrt{3}, multiply the numbers under the square root.

$$4\sqrt{3}+\frac{12\sqrt{6}}{3}$$

Divide 12\sqrt{6} by 3 to get 4\sqrt{6}.

$$4\sqrt{3}+4\sqrt{6}$$

Factor

$$4 {(\sqrt{3} + \sqrt{6})} = 16.726162201$$