Solve 9/2sqrt{25-9*frac{7{15}}}

$$\frac{ 9 }{ 2 \sqrt{ 25-9 \times \frac{ 7 }{ 15 } } }$$

Evaluate

$$\frac{9\sqrt{130}}{104}\approx 0.986690272$$

Solution Steps

Express 9\times \frac{7}{15} as a single fraction.

$$\frac{9}{2\sqrt{25-\frac{9\times 7}{15}}}$$

Multiply 9 and 7 to get 63.

$$\frac{9}{2\sqrt{25-\frac{63}{15}}}$$

Reduce the fraction \frac{63}{15} to lowest terms by extracting and canceling out 3.

$$\frac{9}{2\sqrt{25-\frac{21}{5}}}$$

Convert 25 to fraction \frac{125}{5}.

$$\frac{9}{2\sqrt{\frac{125}{5}-\frac{21}{5}}}$$

Since \frac{125}{5} and \frac{21}{5} have the same denominator, subtract them by subtracting their numerators.

$$\frac{9}{2\sqrt{\frac{125-21}{5}}}$$

Subtract 21 from 125 to get 104.

$$\frac{9}{2\sqrt{\frac{104}{5}}}$$

Rewrite the square root of the division \sqrt{\frac{104}{5}} as the division of square roots \frac{\sqrt{104}}{\sqrt{5}}.

$$\frac{9}{2\times \frac{\sqrt{104}}{\sqrt{5}}}$$

Factor 104=2^{2}\times 26. Rewrite the square root of the product \sqrt{2^{2}\times 26} as the product of square roots \sqrt{2^{2}}\sqrt{26}. Take the square root of 2^{2}.

$$\frac{9}{2\times \frac{2\sqrt{26}}{\sqrt{5}}}$$

Rationalize the denominator of \frac{2\sqrt{26}}{\sqrt{5}} by multiplying numerator and denominator by \sqrt{5}.

$$\frac{9}{2\times \frac{2\sqrt{26}\sqrt{5}}{\left(\sqrt{5}\right)^{2}}}$$

The square of \sqrt{5} is 5.

$$\frac{9}{2\times \frac{2\sqrt{26}\sqrt{5}}{5}}$$

To multiply \sqrt{26} and \sqrt{5}, multiply the numbers under the square root.

$$\frac{9}{2\times \frac{2\sqrt{130}}{5}}$$

Express 2\times \frac{2\sqrt{130}}{5} as a single fraction.

$$\frac{9}{\frac{2\times 2\sqrt{130}}{5}}$$

Divide 9 by \frac{2\times 2\sqrt{130}}{5} by multiplying 9 by the reciprocal of \frac{2\times 2\sqrt{130}}{5}.

$$\frac{9\times 5}{2\times 2\sqrt{130}}$$

Rationalize the denominator of \frac{9\times 5}{2\times 2\sqrt{130}} by multiplying numerator and denominator by \sqrt{130}.

$$\frac{9\times 5\sqrt{130}}{2\times 2\left(\sqrt{130}\right)^{2}}$$

The square of \sqrt{130} is 130.

$$\frac{9\times 5\sqrt{130}}{2\times 2\times 130}$$

Multiply 9 and 5 to get 45.

$$\frac{45\sqrt{130}}{2\times 2\times 130}$$

Multiply 2 and 2 to get 4.

$$\frac{45\sqrt{130}}{4\times 130}$$

Multiply 4 and 130 to get 520.

$$\frac{45\sqrt{130}}{520}$$

Divide 45\sqrt{130} by 520 to get \frac{9}{104}\sqrt{130}.

$$\frac{9}{104}\sqrt{130}$$