Solve 77.500-84*400/sqrt{frac{7410-4761{900}}}

$$\frac { 77.500 - 84 \cdot 400 } { \sqrt { \frac { 7410 - 4761 } { 900 } } }$$

Evaluate

$$-\frac{335225\sqrt{2649}}{883}\approx -19539.645265915$$

Solution Steps

Multiply 84 and 400 to get 33600.

$$\frac{77.5-33600}{\sqrt{\frac{7410-4761}{900}}}$$

Subtract 33600 from 77.5 to get -33522.5.

$$\frac{-33522.5}{\sqrt{\frac{7410-4761}{900}}}$$

Subtract 4761 from 7410 to get 2649.

$$\frac{-33522.5}{\sqrt{\frac{2649}{900}}}$$

Reduce the fraction \frac{2649}{900} to lowest terms by extracting and canceling out 3.

$$\frac{-33522.5}{\sqrt{\frac{883}{300}}}$$

Rewrite the square root of the division \sqrt{\frac{883}{300}} as the division of square roots \frac{\sqrt{883}}{\sqrt{300}}.

$$\frac{-33522.5}{\frac{\sqrt{883}}{\sqrt{300}}}$$

Factor 300=10^{2}\times 3. Rewrite the square root of the product \sqrt{10^{2}\times 3} as the product of square roots \sqrt{10^{2}}\sqrt{3}. Take the square root of 10^{2}.

$$\frac{-33522.5}{\frac{\sqrt{883}}{10\sqrt{3}}}$$

Rationalize the denominator of \frac{\sqrt{883}}{10\sqrt{3}} by multiplying numerator and denominator by \sqrt{3}.

$$\frac{-33522.5}{\frac{\sqrt{883}\sqrt{3}}{10\left(\sqrt{3}\right)^{2}}}$$

The square of \sqrt{3} is 3.

$$\frac{-33522.5}{\frac{\sqrt{883}\sqrt{3}}{10\times 3}}$$

To multiply \sqrt{883} and \sqrt{3}, multiply the numbers under the square root.

$$\frac{-33522.5}{\frac{\sqrt{2649}}{10\times 3}}$$

Multiply 10 and 3 to get 30.

$$\frac{-33522.5}{\frac{\sqrt{2649}}{30}}$$

Divide -33522.5 by \frac{\sqrt{2649}}{30} by multiplying -33522.5 by the reciprocal of \frac{\sqrt{2649}}{30}.

$$\frac{-33522.5\times 30}{\sqrt{2649}}$$

Rationalize the denominator of \frac{-33522.5\times 30}{\sqrt{2649}} by multiplying numerator and denominator by \sqrt{2649}.

$$\frac{-33522.5\times 30\sqrt{2649}}{\left(\sqrt{2649}\right)^{2}}$$

The square of \sqrt{2649} is 2649.

$$\frac{-33522.5\times 30\sqrt{2649}}{2649}$$

Multiply -33522.5 and 30 to get -1005675.

$$\frac{-1005675\sqrt{2649}}{2649}$$

Divide -1005675\sqrt{2649} by 2649 to get -\frac{335225}{883}\sqrt{2649}.

$$-\frac{335225}{883}\sqrt{2649}$$