Solve (sqrt{15}+2sqrt{2})divsqrt{3}

$$( \sqrt { 15 } + 2 \sqrt { 2 } ) \div \sqrt { 3 }$$

Evaluate

$$\frac{2\sqrt{6}}{3}+\sqrt{5}\approx 3.869061139$$

Solution Steps

Rationalize the denominator of \frac{\sqrt{15}+2\sqrt{2}}{\sqrt{3}} by multiplying numerator and denominator by \sqrt{3}.

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

The square of \sqrt{3} is 3.

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

Use the distributive property to multiply \sqrt{15}+2\sqrt{2} by \sqrt{3}.

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

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}.

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

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

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

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

$$\frac{3\sqrt{5}+2\sqrt{6}}{3}$$