Solve 347-85*3/sqrt{(1308-frac{(85)^2{8})(93-72)}}

$$\frac { 347 - 85 \times 3 } { \sqrt { ( 1308 - \frac { ( 85 ) ^ { 2 } } { 8 } ) ( 93 - 72 ) } }$$

Evaluate

$$\frac{184\sqrt{136038}}{68019}\approx 0.997740725$$

Solution Steps

Multiply 85 and 3 to get 255.

$$\frac{347-255}{\sqrt{\left(1308-\frac{85^{2}}{8}\right)\left(93-72\right)}}$$

Subtract 255 from 347 to get 92.

$$\frac{92}{\sqrt{\left(1308-\frac{85^{2}}{8}\right)\left(93-72\right)}}$$

Calculate 85 to the power of 2 and get 7225.

$$\frac{92}{\sqrt{\left(1308-\frac{7225}{8}\right)\left(93-72\right)}}$$

Convert 1308 to fraction \frac{10464}{8}.

$$\frac{92}{\sqrt{\left(\frac{10464}{8}-\frac{7225}{8}\right)\left(93-72\right)}}$$

Since \frac{10464}{8} and \frac{7225}{8} have the same denominator, subtract them by subtracting their numerators.

$$\frac{92}{\sqrt{\frac{10464-7225}{8}\left(93-72\right)}}$$

Subtract 7225 from 10464 to get 3239.

$$\frac{92}{\sqrt{\frac{3239}{8}\left(93-72\right)}}$$

Subtract 72 from 93 to get 21.

$$\frac{92}{\sqrt{\frac{3239}{8}\times 21}}$$

Express \frac{3239}{8}\times 21 as a single fraction.

$$\frac{92}{\sqrt{\frac{3239\times 21}{8}}}$$

Multiply 3239 and 21 to get 68019.

$$\frac{92}{\sqrt{\frac{68019}{8}}}$$

Rewrite the square root of the division \sqrt{\frac{68019}{8}} as the division of square roots \frac{\sqrt{68019}}{\sqrt{8}}.

$$\frac{92}{\frac{\sqrt{68019}}{\sqrt{8}}}$$

Factor 8=2^{2}\times 2. Rewrite the square root of the product \sqrt{2^{2}\times 2} as the product of square roots \sqrt{2^{2}}\sqrt{2}. Take the square root of 2^{2}.

$$\frac{92}{\frac{\sqrt{68019}}{2\sqrt{2}}}$$

Rationalize the denominator of \frac{\sqrt{68019}}{2\sqrt{2}} by multiplying numerator and denominator by \sqrt{2}.

$$\frac{92}{\frac{\sqrt{68019}\sqrt{2}}{2\left(\sqrt{2}\right)^{2}}}$$

The square of \sqrt{2} is 2.

$$\frac{92}{\frac{\sqrt{68019}\sqrt{2}}{2\times 2}}$$

To multiply \sqrt{68019} and \sqrt{2}, multiply the numbers under the square root.

$$\frac{92}{\frac{\sqrt{136038}}{2\times 2}}$$

Multiply 2 and 2 to get 4.

$$\frac{92}{\frac{\sqrt{136038}}{4}}$$

Divide 92 by \frac{\sqrt{136038}}{4} by multiplying 92 by the reciprocal of \frac{\sqrt{136038}}{4}.

$$\frac{92\times 4}{\sqrt{136038}}$$

Rationalize the denominator of \frac{92\times 4}{\sqrt{136038}} by multiplying numerator and denominator by \sqrt{136038}.

$$\frac{92\times 4\sqrt{136038}}{\left(\sqrt{136038}\right)^{2}}$$

The square of \sqrt{136038} is 136038.

$$\frac{92\times 4\sqrt{136038}}{136038}$$

Multiply 92 and 4 to get 368.

$$\frac{368\sqrt{136038}}{136038}$$

Divide 368\sqrt{136038} by 136038 to get \frac{184}{68019}\sqrt{136038}.

$$\frac{184}{68019}\sqrt{136038}$$