Solve 347-85*3/sqrt{(308-frac{851{8})^4(93-24)}}

$$\frac { 347 - 85 \times 3 } { \sqrt { ( 308 - \frac { 851 } { 8 } ) ^ { 4 } ( 93 - 24 ) } }$$

Evaluate

$$\frac{256\sqrt{69}}{7805307}\approx 0.000272442$$

Solution Steps

Multiply 85 and 3 to get 255.

$$\frac{347-255}{\sqrt{\left(308-\frac{851}{8}\right)^{4}\left(93-24\right)}}$$

Subtract 255 from 347 to get 92.

$$\frac{92}{\sqrt{\left(308-\frac{851}{8}\right)^{4}\left(93-24\right)}}$$

Subtract \frac{851}{8} from 308 to get \frac{1613}{8}.

$$\frac{92}{\sqrt{\left(\frac{1613}{8}\right)^{4}\left(93-24\right)}}$$

Calculate \frac{1613}{8} to the power of 4 and get \frac{6769201929361}{4096}.

$$\frac{92}{\sqrt{\frac{6769201929361}{4096}\left(93-24\right)}}$$

Subtract 24 from 93 to get 69.

$$\frac{92}{\sqrt{\frac{6769201929361}{4096}\times 69}}$$

Multiply \frac{6769201929361}{4096} and 69 to get \frac{467074933125909}{4096}.

$$\frac{92}{\sqrt{\frac{467074933125909}{4096}}}$$

Rewrite the square root of the division \sqrt{\frac{467074933125909}{4096}} as the division of square roots \frac{\sqrt{467074933125909}}{\sqrt{4096}}.

$$\frac{92}{\frac{\sqrt{467074933125909}}{\sqrt{4096}}}$$

Factor 467074933125909=2601769^{2}\times 69. Rewrite the square root of the product \sqrt{2601769^{2}\times 69} as the product of square roots \sqrt{2601769^{2}}\sqrt{69}. Take the square root of 2601769^{2}.

$$\frac{92}{\frac{2601769\sqrt{69}}{\sqrt{4096}}}$$

Calculate the square root of 4096 and get 64.

$$\frac{92}{\frac{2601769\sqrt{69}}{64}}$$

Divide 92 by \frac{2601769\sqrt{69}}{64} by multiplying 92 by the reciprocal of \frac{2601769\sqrt{69}}{64}.

$$\frac{92\times 64}{2601769\sqrt{69}}$$

Rationalize the denominator of \frac{92\times 64}{2601769\sqrt{69}} by multiplying numerator and denominator by \sqrt{69}.

$$\frac{92\times 64\sqrt{69}}{2601769\left(\sqrt{69}\right)^{2}}$$

The square of \sqrt{69} is 69.

$$\frac{92\times 64\sqrt{69}}{2601769\times 69}$$

Multiply 92 and 64 to get 5888.

$$\frac{5888\sqrt{69}}{2601769\times 69}$$

Multiply 2601769 and 69 to get 179522061.

$$\frac{5888\sqrt{69}}{179522061}$$

Divide 5888\sqrt{69} by 179522061 to get \frac{256}{7805307}\sqrt{69}.

$$\frac{256}{7805307}\sqrt{69}$$