Solve sqrt{60/760*101325*2/13546-800}

$$\sqrt { \frac { \frac { 60 } { 760 } \times 101325 \times 2 } { 13546 - 800 } }$$

Evaluate

$$\frac{15\sqrt{327177074}}{242174}\approx 1.12035376$$

Solution Steps

Reduce the fraction \frac{60}{760} to lowest terms by extracting and canceling out 20.

$$\sqrt{\frac{\frac{3}{38}\times 101325\times 2}{13546-800}}$$

Express \frac{3}{38}\times 101325 as a single fraction.

$$\sqrt{\frac{\frac{3\times 101325}{38}\times 2}{13546-800}}$$

Multiply 3 and 101325 to get 303975.

$$\sqrt{\frac{\frac{303975}{38}\times 2}{13546-800}}$$

Express \frac{303975}{38}\times 2 as a single fraction.

$$\sqrt{\frac{\frac{303975\times 2}{38}}{13546-800}}$$

Multiply 303975 and 2 to get 607950.

$$\sqrt{\frac{\frac{607950}{38}}{13546-800}}$$

Reduce the fraction \frac{607950}{38} to lowest terms by extracting and canceling out 2.

$$\sqrt{\frac{\frac{303975}{19}}{13546-800}}$$

Subtract 800 from 13546 to get 12746.

$$\sqrt{\frac{\frac{303975}{19}}{12746}}$$

Express \frac{\frac{303975}{19}}{12746} as a single fraction.

$$\sqrt{\frac{303975}{19\times 12746}}$$

Multiply 19 and 12746 to get 242174.

$$\sqrt{\frac{303975}{242174}}$$

Rewrite the square root of the division \sqrt{\frac{303975}{242174}} as the division of square roots \frac{\sqrt{303975}}{\sqrt{242174}}.

$$\frac{\sqrt{303975}}{\sqrt{242174}}$$

Factor 303975=15^{2}\times 1351. Rewrite the square root of the product \sqrt{15^{2}\times 1351} as the product of square roots \sqrt{15^{2}}\sqrt{1351}. Take the square root of 15^{2}.

$$\frac{15\sqrt{1351}}{\sqrt{242174}}$$

Rationalize the denominator of \frac{15\sqrt{1351}}{\sqrt{242174}} by multiplying numerator and denominator by \sqrt{242174}.

$$\frac{15\sqrt{1351}\sqrt{242174}}{\left(\sqrt{242174}\right)^{2}}$$

The square of \sqrt{242174} is 242174.

$$\frac{15\sqrt{1351}\sqrt{242174}}{242174}$$

To multiply \sqrt{1351} and \sqrt{242174}, multiply the numbers under the square root.

$$\frac{15\sqrt{327177074}}{242174}$$