Solve 1+8/sqrt{frac{113{359}}}

$$1+ \frac{ 8 }{ \sqrt{ \frac{ 113 }{ 359 } } }$$

Evaluate

$$\frac{8\sqrt{40567}}{113}+1\approx 15.259292887$$

Solution Steps

Rewrite the square root of the division \sqrt{\frac{113}{359}} as the division of square roots \frac{\sqrt{113}}{\sqrt{359}}.

$$1+\frac{8}{\frac{\sqrt{113}}{\sqrt{359}}}$$

Rationalize the denominator of \frac{\sqrt{113}}{\sqrt{359}} by multiplying numerator and denominator by \sqrt{359}.

$$1+\frac{8}{\frac{\sqrt{113}\sqrt{359}}{\left(\sqrt{359}\right)^{2}}}$$

The square of \sqrt{359} is 359.

$$1+\frac{8}{\frac{\sqrt{113}\sqrt{359}}{359}}$$

To multiply \sqrt{113} and \sqrt{359}, multiply the numbers under the square root.

$$1+\frac{8}{\frac{\sqrt{40567}}{359}}$$

Divide 8 by \frac{\sqrt{40567}}{359} by multiplying 8 by the reciprocal of \frac{\sqrt{40567}}{359}.

$$1+\frac{8\times 359}{\sqrt{40567}}$$

Rationalize the denominator of \frac{8\times 359}{\sqrt{40567}} by multiplying numerator and denominator by \sqrt{40567}.

$$1+\frac{8\times 359\sqrt{40567}}{\left(\sqrt{40567}\right)^{2}}$$

The square of \sqrt{40567} is 40567.

$$1+\frac{8\times 359\sqrt{40567}}{40567}$$

Multiply 8 and 359 to get 2872.

$$1+\frac{2872\sqrt{40567}}{40567}$$

Divide 2872\sqrt{40567} by 40567 to get \frac{8}{113}\sqrt{40567}.

$$1+\frac{8}{113}\sqrt{40567}$$