Solve sqrt{1-12/25+60/169/2}

$$\sqrt { \frac { 1 - \frac { 12 } { 25 } + \frac { 60 } { 169 } } { 2 } }$$

Evaluate

$$\frac{\sqrt{7394}}{130}\approx 0.66144901$$

Solution Steps

Convert 1 to fraction \frac{25}{25}.

$$\sqrt{\frac{\frac{25}{25}-\frac{12}{25}+\frac{60}{169}}{2}}$$

Since \frac{25}{25} and \frac{12}{25} have the same denominator, subtract them by subtracting their numerators.

$$\sqrt{\frac{\frac{25-12}{25}+\frac{60}{169}}{2}}$$

Subtract 12 from 25 to get 13.

$$\sqrt{\frac{\frac{13}{25}+\frac{60}{169}}{2}}$$

Least common multiple of 25 and 169 is 4225. Convert \frac{13}{25} and \frac{60}{169} to fractions with denominator 4225.

$$\sqrt{\frac{\frac{2197}{4225}+\frac{1500}{4225}}{2}}$$

Since \frac{2197}{4225} and \frac{1500}{4225} have the same denominator, add them by adding their numerators.

$$\sqrt{\frac{\frac{2197+1500}{4225}}{2}}$$

Add 2197 and 1500 to get 3697.

$$\sqrt{\frac{\frac{3697}{4225}}{2}}$$

Express \frac{\frac{3697}{4225}}{2} as a single fraction.

$$\sqrt{\frac{3697}{4225\times 2}}$$

Multiply 4225 and 2 to get 8450.

$$\sqrt{\frac{3697}{8450}}$$

Rewrite the square root of the division \sqrt{\frac{3697}{8450}} as the division of square roots \frac{\sqrt{3697}}{\sqrt{8450}}.

$$\frac{\sqrt{3697}}{\sqrt{8450}}$$

Factor 8450=65^{2}\times 2. Rewrite the square root of the product \sqrt{65^{2}\times 2} as the product of square roots \sqrt{65^{2}}\sqrt{2}. Take the square root of 65^{2}.

$$\frac{\sqrt{3697}}{65\sqrt{2}}$$

Rationalize the denominator of \frac{\sqrt{3697}}{65\sqrt{2}} by multiplying numerator and denominator by \sqrt{2}.

$$\frac{\sqrt{3697}\sqrt{2}}{65\left(\sqrt{2}\right)^{2}}$$

The square of \sqrt{2} is 2.

$$\frac{\sqrt{3697}\sqrt{2}}{65\times 2}$$

To multiply \sqrt{3697} and \sqrt{2}, multiply the numbers under the square root.

$$\frac{\sqrt{7394}}{65\times 2}$$

Multiply 65 and 2 to get 130.

$$\frac{\sqrt{7394}}{130}$$