Solve sqrt{((25divfrac{23/3)/8+1*(2-1)}}{111}

$$\frac { \sqrt { ( \frac { ( 25 \div \frac { 23 } { 3 } ) } { 8 + 1 \times ( 2 - 1 ) } } } { 111 }$$

Evaluate

$$\frac{5\sqrt{69}}{7659}\approx 0.005422786$$

Solution Steps

Divide 25 by \frac{23}{3} by multiplying 25 by the reciprocal of \frac{23}{3}.

$$\frac{\sqrt{\frac{25\times \frac{3}{23}}{8+1\left(2-1\right)}}}{111}$$

Express 25\times \frac{3}{23} as a single fraction.

$$\frac{\sqrt{\frac{\frac{25\times 3}{23}}{8+1\left(2-1\right)}}}{111}$$

Multiply 25 and 3 to get 75.

$$\frac{\sqrt{\frac{\frac{75}{23}}{8+1\left(2-1\right)}}}{111}$$

Subtract 1 from 2 to get 1.

$$\frac{\sqrt{\frac{\frac{75}{23}}{8+1\times 1}}}{111}$$

Multiply 1 and 1 to get 1.

$$\frac{\sqrt{\frac{\frac{75}{23}}{8+1}}}{111}$$

Add 8 and 1 to get 9.

$$\frac{\sqrt{\frac{\frac{75}{23}}{9}}}{111}$$

Express \frac{\frac{75}{23}}{9} as a single fraction.

$$\frac{\sqrt{\frac{75}{23\times 9}}}{111}$$

Multiply 23 and 9 to get 207.

$$\frac{\sqrt{\frac{75}{207}}}{111}$$

Reduce the fraction \frac{75}{207} to lowest terms by extracting and canceling out 3.

$$\frac{\sqrt{\frac{25}{69}}}{111}$$

Rewrite the square root of the division \sqrt{\frac{25}{69}} as the division of square roots \frac{\sqrt{25}}{\sqrt{69}}.

$$\frac{\frac{\sqrt{25}}{\sqrt{69}}}{111}$$

Calculate the square root of 25 and get 5.

$$\frac{\frac{5}{\sqrt{69}}}{111}$$

Rationalize the denominator of \frac{5}{\sqrt{69}} by multiplying numerator and denominator by \sqrt{69}.

$$\frac{\frac{5\sqrt{69}}{\left(\sqrt{69}\right)^{2}}}{111}$$

The square of \sqrt{69} is 69.

$$\frac{\frac{5\sqrt{69}}{69}}{111}$$

Express \frac{\frac{5\sqrt{69}}{69}}{111} as a single fraction.

$$\frac{5\sqrt{69}}{69\times 111}$$

Multiply 69 and 111 to get 7659.

$$\frac{5\sqrt{69}}{7659}$$