Solve sqrt{0.027div15.36/55696}

$$\sqrt { 0.027 \div \frac { 15.36 } { 55696 } }$$

Evaluate

$$\frac{177\sqrt{5}}{40}\approx 9.8946008$$

Solution Steps

Divide 0.027 by \frac{15.36}{55696} by multiplying 0.027 by the reciprocal of \frac{15.36}{55696}.

$$\sqrt{\frac{0.027\times 55696}{15.36}}$$

Multiply 0.027 and 55696 to get 1503.792.

$$\sqrt{\frac{1503.792}{15.36}}$$

Expand \frac{1503.792}{15.36} by multiplying both numerator and the denominator by 1000.

$$\sqrt{\frac{1503792}{15360}}$$

Reduce the fraction \frac{1503792}{15360} to lowest terms by extracting and canceling out 48.

$$\sqrt{\frac{31329}{320}}$$

Rewrite the square root of the division \sqrt{\frac{31329}{320}} as the division of square roots \frac{\sqrt{31329}}{\sqrt{320}}.

$$\frac{\sqrt{31329}}{\sqrt{320}}$$

Calculate the square root of 31329 and get 177.

$$\frac{177}{\sqrt{320}}$$

Factor 320=8^{2}\times 5. Rewrite the square root of the product \sqrt{8^{2}\times 5} as the product of square roots \sqrt{8^{2}}\sqrt{5}. Take the square root of 8^{2}.

$$\frac{177}{8\sqrt{5}}$$

Rationalize the denominator of \frac{177}{8\sqrt{5}} by multiplying numerator and denominator by \sqrt{5}.

$$\frac{177\sqrt{5}}{8\left(\sqrt{5}\right)^{2}}$$

The square of \sqrt{5} is 5.

$$\frac{177\sqrt{5}}{8\times 5}$$

Multiply 8 and 5 to get 40.

$$\frac{177\sqrt{5}}{40}$$