Solve sqrt{5}div(sqrt{3})^2+(sqrt{5})^3div(sqrt{5})^2

$$\sqrt { 5 } \div ( \sqrt { 3 } ) ^ { 2 } + ( \sqrt { 5 } ) ^ { 3 } \div ( \sqrt { 5 } ) ^ { 2 }$$

Evaluate

$$\frac{4\sqrt{5}}{3}\approx 2.98142397$$

Solution Steps

To divide powers of the same base, subtract the denominator's exponent from the numerator's exponent. Subtract 2 from 3 to get 1.

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

The square of \sqrt{3} is 3.

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

Calculate \sqrt{5} to the power of 1 and get \sqrt{5}.

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

Combine \frac{\sqrt{5}}{3} and \sqrt{5} to get \frac{4}{3}\sqrt{5}.

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