Solve 3.8-3.3/0.53/sqrt{177}=

$$\frac { 3.8 - 3.3 } { 0.53 / \sqrt { 177 } } =$$

Evaluate

$$\frac{50\sqrt{177}}{53}\approx 12.551070468$$

Solution Steps

Subtract 3.3 from 3.8 to get 0.5.

$$\frac{0.5}{\frac{0.53}{\sqrt{177}}}$$

Rationalize the denominator of \frac{0.53}{\sqrt{177}} by multiplying numerator and denominator by \sqrt{177}.

$$\frac{0.5}{\frac{0.53\sqrt{177}}{\left(\sqrt{177}\right)^{2}}}$$

The square of \sqrt{177} is 177.

$$\frac{0.5}{\frac{0.53\sqrt{177}}{177}}$$

Divide 0.53\sqrt{177} by 177 to get \frac{53}{17700}\sqrt{177}.

$$\frac{0.5}{\frac{53}{17700}\sqrt{177}}$$

Rationalize the denominator of \frac{0.5}{\frac{53}{17700}\sqrt{177}} by multiplying numerator and denominator by \sqrt{177}.

$$\frac{0.5\sqrt{177}}{\frac{53}{17700}\left(\sqrt{177}\right)^{2}}$$

The square of \sqrt{177} is 177.

$$\frac{0.5\sqrt{177}}{\frac{53}{17700}\times 177}$$

Multiply \frac{53}{17700} and 177 to get 0.53.

$$\frac{0.5\sqrt{177}}{0.53}$$

Divide 0.5\sqrt{177} by 0.53 to get \frac{50}{53}\sqrt{177}.

$$\frac{50}{53}\sqrt{177}$$