Solve (2.5div2):729div(1+sqrt{15}-1)

$$( 2.5 \div 2 ) : 729 \div ( 1 + \sqrt { 15 } - 1 )$$

Evaluate

$$\frac{\sqrt{15}}{8748}\approx 0.000442728$$

Solution Steps

Express \frac{\frac{2.5}{2}}{729} as a single fraction.

$$\frac{\frac{2.5}{2\times 729}}{1+\sqrt{15}-1}$$

Multiply 2 and 729 to get 1458.

$$\frac{\frac{2.5}{1458}}{1+\sqrt{15}-1}$$

Expand \frac{2.5}{1458} by multiplying both numerator and the denominator by 10.

$$\frac{\frac{25}{14580}}{1+\sqrt{15}-1}$$

Reduce the fraction \frac{25}{14580} to lowest terms by extracting and canceling out 5.

$$\frac{\frac{5}{2916}}{1+\sqrt{15}-1}$$

Subtract 1 from 1 to get 0.

$$\frac{\frac{5}{2916}}{\sqrt{15}}$$

Express \frac{\frac{5}{2916}}{\sqrt{15}} as a single fraction.

$$\frac{5}{2916\sqrt{15}}$$

Rationalize the denominator of \frac{5}{2916\sqrt{15}} by multiplying numerator and denominator by \sqrt{15}.

$$\frac{5\sqrt{15}}{2916\left(\sqrt{15}\right)^{2}}$$

The square of \sqrt{15} is 15.

$$\frac{5\sqrt{15}}{2916\times 15}$$

Cancel out 5 in both numerator and denominator.

$$\frac{\sqrt{15}}{3\times 2916}$$

Multiply 3 and 2916 to get 8748.

$$\frac{\sqrt{15}}{8748}$$