Solve 4.816/sqrt{40}=

$$4.816 / \sqrt { 40 } =$$

Evaluate

$$\frac{301\sqrt{10}}{1250}\approx 0.761476461$$

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}.

$$\frac{4.816}{2\sqrt{10}}$$

Rationalize the denominator of \frac{4.816}{2\sqrt{10}} by multiplying numerator and denominator by \sqrt{10}.

$$\frac{4.816\sqrt{10}}{2\left(\sqrt{10}\right)^{2}}$$

The square of \sqrt{10} is 10.

$$\frac{4.816\sqrt{10}}{2\times 10}$$

Multiply 2 and 10 to get 20.

$$\frac{4.816\sqrt{10}}{20}$$

Divide 4.816\sqrt{10} by 20 to get 0.2408\sqrt{10}.

$$0.2408\sqrt{10}$$