Solve 2sqrt{3}divsqrt{3}+4sqrt{15}divsqrt{3}

$$2 \sqrt { 3 } \div \sqrt { 3 } + 4 \sqrt { 15 } \div \sqrt { 3 }$$

Evaluate

$$4\sqrt{5}+2\approx 10.94427191$$

Solution Steps

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

$$\frac{2\sqrt{3}\sqrt{3}}{\left(\sqrt{3}\right)^{2}}+\frac{4\sqrt{15}}{\sqrt{3}}$$

The square of \sqrt{3} is 3.

$$\frac{2\sqrt{3}\sqrt{3}}{3}+\frac{4\sqrt{15}}{\sqrt{3}}$$

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

$$\frac{2\times 3}{3}+\frac{4\sqrt{15}}{\sqrt{3}}$$

Multiply 2 and 3 to get 6.

$$\frac{6}{3}+\frac{4\sqrt{15}}{\sqrt{3}}$$

Divide 6 by 3 to get 2.

$$2+\frac{4\sqrt{15}}{\sqrt{3}}$$

Rationalize the denominator of \frac{4\sqrt{15}}{\sqrt{3}} by multiplying numerator and denominator by \sqrt{3}.

$$2+\frac{4\sqrt{15}\sqrt{3}}{\left(\sqrt{3}\right)^{2}}$$

The square of \sqrt{3} is 3.

$$2+\frac{4\sqrt{15}\sqrt{3}}{3}$$

Factor 15=3\times 5. Rewrite the square root of the product \sqrt{3\times 5} as the product of square roots \sqrt{3}\sqrt{5}.

$$2+\frac{4\sqrt{3}\sqrt{5}\sqrt{3}}{3}$$

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

$$2+\frac{4\times 3\sqrt{5}}{3}$$

Cancel out 3 and 3.

$$2+4\sqrt{5}$$

Factor

$$2 {(2 \sqrt{5} + 1)} = 10.94427191$$