Solve sqrt{[(23/12)*(1/15)+8/9]:13/20}

$$\sqrt { [ ( \frac { 23 } { 12 } ) \times ( \frac { 1 } { 15 } ) + \frac { 8 } { 9 } ] : \frac { 13 } { 20 } }$$

Evaluate

$$\frac{\sqrt{2379}}{39}\approx 1.250640861$$

Solution Steps

Multiply \frac{23}{12} times \frac{1}{15} by multiplying numerator times numerator and denominator times denominator.

$$\sqrt{\frac{\frac{23\times 1}{12\times 15}+\frac{8}{9}}{\frac{13}{20}}}$$

Do the multiplications in the fraction \frac{23\times 1}{12\times 15}.

$$\sqrt{\frac{\frac{23}{180}+\frac{8}{9}}{\frac{13}{20}}}$$

Least common multiple of 180 and 9 is 180. Convert \frac{23}{180} and \frac{8}{9} to fractions with denominator 180.

$$\sqrt{\frac{\frac{23}{180}+\frac{160}{180}}{\frac{13}{20}}}$$

Since \frac{23}{180} and \frac{160}{180} have the same denominator, add them by adding their numerators.

$$\sqrt{\frac{\frac{23+160}{180}}{\frac{13}{20}}}$$

Add 23 and 160 to get 183.

$$\sqrt{\frac{\frac{183}{180}}{\frac{13}{20}}}$$

Reduce the fraction \frac{183}{180} to lowest terms by extracting and canceling out 3.

$$\sqrt{\frac{\frac{61}{60}}{\frac{13}{20}}}$$

Divide \frac{61}{60} by \frac{13}{20} by multiplying \frac{61}{60} by the reciprocal of \frac{13}{20}.

$$\sqrt{\frac{61}{60}\times \frac{20}{13}}$$

Multiply \frac{61}{60} times \frac{20}{13} by multiplying numerator times numerator and denominator times denominator.

$$\sqrt{\frac{61\times 20}{60\times 13}}$$

Do the multiplications in the fraction \frac{61\times 20}{60\times 13}.

$$\sqrt{\frac{1220}{780}}$$

Reduce the fraction \frac{1220}{780} to lowest terms by extracting and canceling out 20.

$$\sqrt{\frac{61}{39}}$$

Rewrite the square root of the division \sqrt{\frac{61}{39}} as the division of square roots \frac{\sqrt{61}}{\sqrt{39}}.

$$\frac{\sqrt{61}}{\sqrt{39}}$$

Rationalize the denominator of \frac{\sqrt{61}}{\sqrt{39}} by multiplying numerator and denominator by \sqrt{39}.

$$\frac{\sqrt{61}\sqrt{39}}{\left(\sqrt{39}\right)^{2}}$$

The square of \sqrt{39} is 39.

$$\frac{\sqrt{61}\sqrt{39}}{39}$$

To multiply \sqrt{61} and \sqrt{39}, multiply the numbers under the square root.

$$\frac{\sqrt{2379}}{39}$$