Solve sqrt{6.8-4.73/8.95}=

$$\sqrt { \frac { 6.8 - 4.73 } { 8.95 } } =$$

Evaluate

$$\frac{3\sqrt{20585}}{895}\approx 0.480920904$$

Solution Steps

Subtract 4.73 from 6.8 to get 2.07.

$$\sqrt{\frac{2.07}{8.95}}$$

Expand \frac{2.07}{8.95} by multiplying both numerator and the denominator by 100.

$$\sqrt{\frac{207}{895}}$$

Rewrite the square root of the division \sqrt{\frac{207}{895}} as the division of square roots \frac{\sqrt{207}}{\sqrt{895}}.

$$\frac{\sqrt{207}}{\sqrt{895}}$$

Factor 207=3^{2}\times 23. Rewrite the square root of the product \sqrt{3^{2}\times 23} as the product of square roots \sqrt{3^{2}}\sqrt{23}. Take the square root of 3^{2}.

$$\frac{3\sqrt{23}}{\sqrt{895}}$$

Rationalize the denominator of \frac{3\sqrt{23}}{\sqrt{895}} by multiplying numerator and denominator by \sqrt{895}.

$$\frac{3\sqrt{23}\sqrt{895}}{\left(\sqrt{895}\right)^{2}}$$

The square of \sqrt{895} is 895.

$$\frac{3\sqrt{23}\sqrt{895}}{895}$$

To multiply \sqrt{23} and \sqrt{895}, multiply the numbers under the square root.

$$\frac{3\sqrt{20585}}{895}$$