Solve a/sqrt{40}=

$$\frac { a } { \sqrt { 40 } } =$$

Evaluate

$$\frac{\sqrt{10}a}{20}$$

Solution Steps

Factor 40=2^{2}\times 10. Rewrite the square root of the product \sqrt{2^{2}\times 10} as the product of square roots \sqrt{2^{2}}\sqrt{10}. Take the square root of 2^{2}.

$$\frac{a}{2\sqrt{10}}$$

Rationalize the denominator of \frac{a}{2\sqrt{10}} by multiplying numerator and denominator by \sqrt{10}.

$$\frac{a\sqrt{10}}{2\left(\sqrt{10}\right)^{2}}$$

The square of \sqrt{10} is 10.

$$\frac{a\sqrt{10}}{2\times 10}$$

Multiply 2 and 10 to get 20.

$$\frac{a\sqrt{10}}{20}$$

Differentiate w.r.t. a

$$\frac{\sqrt{10}}{20} = 0.15811388300841897$$