Solve frac{8+sqrt{3}*1}{sqrt{5}}

$$\frac{ 8+ \sqrt{ 3 } \times 1 }{ \sqrt{ 5 } }$$

Evaluate

$$\frac{\sqrt{5}\left(\sqrt{3}+8\right)}{5}\approx 4.352305433$$

Solution Steps

Rationalize the denominator of \frac{8+1\sqrt{3}}{\sqrt{5}} by multiplying numerator and denominator by \sqrt{5}.

$$\frac{\left(8+1\sqrt{3}\right)\sqrt{5}}{\left(\sqrt{5}\right)^{2}}$$

The square of \sqrt{5} is 5.

$$\frac{\left(8+1\sqrt{3}\right)\sqrt{5}}{5}$$

Use the distributive property to multiply 8+1\sqrt{3} by \sqrt{5}.

$$\frac{8\sqrt{5}+1\sqrt{3}\sqrt{5}}{5}$$

To multiply \sqrt{3} and \sqrt{5}, multiply the numbers under the square root.

$$\frac{8\sqrt{5}+1\sqrt{15}}{5}$$

For any term t, t\times 1=t and 1t=t.

$$\frac{8\sqrt{5}+\sqrt{15}}{5}$$