Solve frac{73sqrt{5}}{2}*frac{7-3sqrt{5}}{2}

$$\frac { 73 \sqrt { 5 } } { 2 } \times \frac { 7 - 3 \sqrt { 5 } } { 2 }$$

Evaluate

$$\frac{511\sqrt{5}-1095}{4}\approx 11.907684126$$

Solution Steps

Multiply \frac{73\sqrt{5}}{2} times \frac{7-3\sqrt{5}}{2} by multiplying numerator times numerator and denominator times denominator.

$$\frac{73\sqrt{5}\left(7-3\sqrt{5}\right)}{2\times 2}$$

Multiply 2 and 2 to get 4.

$$\frac{73\sqrt{5}\left(7-3\sqrt{5}\right)}{4}$$

Use the distributive property to multiply 73\sqrt{5} by 7-3\sqrt{5}.

$$\frac{511\sqrt{5}-219\left(\sqrt{5}\right)^{2}}{4}$$

The square of \sqrt{5} is 5.

$$\frac{511\sqrt{5}-219\times 5}{4}$$

Multiply -219 and 5 to get -1095.

$$\frac{511\sqrt{5}-1095}{4}$$

Factor

$$\frac{73 {(7 \sqrt{5} - 15)}}{4} = 11.907684125598148$$