Solve 1+0.5-18/2.80.23/0.55/sqrt{7*10^-3frac{18{2.8}}}

$$\frac{ 1+0.5- \frac{ 18 }{ 2.8 } \frac{ 0.23 }{ 0.55 } }{ \sqrt{ 7 \times { 10 }^{ -3 } \frac{ 18 }{ 2.8 } } }$$

Evaluate

$$-\frac{61\sqrt{200}}{154}\approx -5.60175502$$

Solution Steps

Add 1 and 0.5 to get 1.5.

$$\frac{1.5-\frac{18}{2.8}\times \frac{0.23}{0.55}}{\sqrt{7\times 10^{-3}\times \frac{18}{2.8}}}$$

Expand \frac{18}{2.8} by multiplying both numerator and the denominator by 10.

$$\frac{1.5-\frac{180}{28}\times \frac{0.23}{0.55}}{\sqrt{7\times 10^{-3}\times \frac{18}{2.8}}}$$

Reduce the fraction \frac{180}{28} to lowest terms by extracting and canceling out 4.

$$\frac{1.5-\frac{45}{7}\times \frac{0.23}{0.55}}{\sqrt{7\times 10^{-3}\times \frac{18}{2.8}}}$$

Expand \frac{0.23}{0.55} by multiplying both numerator and the denominator by 100.

$$\frac{1.5-\frac{45}{7}\times \frac{23}{55}}{\sqrt{7\times 10^{-3}\times \frac{18}{2.8}}}$$

Multiply \frac{45}{7} and \frac{23}{55} to get \frac{207}{77}.

$$\frac{1.5-\frac{207}{77}}{\sqrt{7\times 10^{-3}\times \frac{18}{2.8}}}$$

Subtract \frac{207}{77} from 1.5 to get -\frac{183}{154}.

$$\frac{-\frac{183}{154}}{\sqrt{7\times 10^{-3}\times \frac{18}{2.8}}}$$

Calculate 10 to the power of -3 and get \frac{1}{1000}.

$$\frac{-\frac{183}{154}}{\sqrt{7\times \frac{1}{1000}\times \frac{18}{2.8}}}$$

Multiply 7 and \frac{1}{1000} to get \frac{7}{1000}.

$$\frac{-\frac{183}{154}}{\sqrt{\frac{7}{1000}\times \frac{18}{2.8}}}$$

Expand \frac{18}{2.8} by multiplying both numerator and the denominator by 10.

$$\frac{-\frac{183}{154}}{\sqrt{\frac{7}{1000}\times \frac{180}{28}}}$$

Reduce the fraction \frac{180}{28} to lowest terms by extracting and canceling out 4.

$$\frac{-\frac{183}{154}}{\sqrt{\frac{7}{1000}\times \frac{45}{7}}}$$

Multiply \frac{7}{1000} and \frac{45}{7} to get \frac{9}{200}.

$$\frac{-\frac{183}{154}}{\sqrt{\frac{9}{200}}}$$

Rewrite the square root of the division \sqrt{\frac{9}{200}} as the division of square roots \frac{\sqrt{9}}{\sqrt{200}}.

$$\frac{-\frac{183}{154}}{\frac{\sqrt{9}}{\sqrt{200}}}$$

Calculate the square root of 9 and get 3.

$$\frac{-\frac{183}{154}}{\frac{3}{\sqrt{200}}}$$

Factor 200=10^{2}\times 2. Rewrite the square root of the product \sqrt{10^{2}\times 2} as the product of square roots \sqrt{10^{2}}\sqrt{2}. Take the square root of 10^{2}.

$$\frac{-\frac{183}{154}}{\frac{3}{10\sqrt{2}}}$$

Rationalize the denominator of \frac{3}{10\sqrt{2}} by multiplying numerator and denominator by \sqrt{2}.

$$\frac{-\frac{183}{154}}{\frac{3\sqrt{2}}{10\left(\sqrt{2}\right)^{2}}}$$

The square of \sqrt{2} is 2.

$$\frac{-\frac{183}{154}}{\frac{3\sqrt{2}}{10\times 2}}$$

Multiply 10 and 2 to get 20.

$$\frac{-\frac{183}{154}}{\frac{3\sqrt{2}}{20}}$$

Divide -\frac{183}{154} by \frac{3\sqrt{2}}{20} by multiplying -\frac{183}{154} by the reciprocal of \frac{3\sqrt{2}}{20}.

$$\frac{-183\times 20}{154\times 3\sqrt{2}}$$

Cancel out 2\times 3 in both numerator and denominator.

$$\frac{-61\times 10}{77\sqrt{2}}$$

Rationalize the denominator of \frac{-61\times 10}{77\sqrt{2}} by multiplying numerator and denominator by \sqrt{2}.

$$\frac{-61\times 10\sqrt{2}}{77\left(\sqrt{2}\right)^{2}}$$

The square of \sqrt{2} is 2.

$$\frac{-61\times 10\sqrt{2}}{77\times 2}$$

Multiply -61 and 10 to get -610.

$$\frac{-610\sqrt{2}}{77\times 2}$$

Multiply 77 and 2 to get 154.

$$\frac{-610\sqrt{2}}{154}$$

Divide -610\sqrt{2} by 154 to get -\frac{305}{77}\sqrt{2}.

$$-\frac{305}{77}\sqrt{2}$$