Solve x^5/sqrt{45}=?

$$\frac { x ^ { 5 } } { \sqrt { 45 } } = ?$$

Evaluate

$$\frac{\sqrt{5}x^{5}}{15}$$

Solution Steps

Factor 45=3^{2}\times 5. Rewrite the square root of the product \sqrt{3^{2}\times 5} as the product of square roots \sqrt{3^{2}}\sqrt{5}. Take the square root of 3^{2}.

$$\frac{x^{5}}{3\sqrt{5}}$$

Rationalize the denominator of \frac{x^{5}}{3\sqrt{5}} by multiplying numerator and denominator by \sqrt{5}.

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

The square of \sqrt{5} is 5.

$$\frac{x^{5}\sqrt{5}}{3\times 5}$$

Multiply 3 and 5 to get 15.

$$\frac{x^{5}\sqrt{5}}{15}$$

Differentiate w.r.t. x

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