Solve 4.62-5/frac{.92{sqrt{45}}}

$$\frac{ 4.62-5 }{ \frac{ .92 }{ \sqrt{ 45 } } }$$

Evaluate

$$-\frac{57\sqrt{5}}{46}\approx -2.770779885$$

Solution Steps

Subtract 5 from 4.62 to get -0.38.

$$\frac{-0.38}{\frac{0.92}{\sqrt{45}}}$$

Factor 45=3^{2}\times 5. Rewrite the square root of the product \sqrt{3^{2}\times 5} as the product of square roots \sqrt{3^{2}}\sqrt{5}. Take the square root of 3^{2}.

$$\frac{-0.38}{\frac{0.92}{3\sqrt{5}}}$$

Rationalize the denominator of \frac{0.92}{3\sqrt{5}} by multiplying numerator and denominator by \sqrt{5}.

$$\frac{-0.38}{\frac{0.92\sqrt{5}}{3\left(\sqrt{5}\right)^{2}}}$$

The square of \sqrt{5} is 5.

$$\frac{-0.38}{\frac{0.92\sqrt{5}}{3\times 5}}$$

Multiply 3 and 5 to get 15.

$$\frac{-0.38}{\frac{0.92\sqrt{5}}{15}}$$

Divide 0.92\sqrt{5} by 15 to get \frac{23}{375}\sqrt{5}.

$$\frac{-0.38}{\frac{23}{375}\sqrt{5}}$$

Rationalize the denominator of \frac{-0.38}{\frac{23}{375}\sqrt{5}} by multiplying numerator and denominator by \sqrt{5}.

$$\frac{-0.38\sqrt{5}}{\frac{23}{375}\left(\sqrt{5}\right)^{2}}$$

The square of \sqrt{5} is 5.

$$\frac{-0.38\sqrt{5}}{\frac{23}{375}\times 5}$$

Multiply \frac{23}{375} and 5 to get \frac{23}{75}.

$$\frac{-0.38\sqrt{5}}{\frac{23}{75}}$$

Divide -0.38\sqrt{5} by \frac{23}{75} to get -\frac{57}{46}\sqrt{5}.

$$-\frac{57}{46}\sqrt{5}$$