Solve (5-3sqrt{3})*(5-frac{9sqrt{3}}{2})=

$$(5-3 \sqrt{ 3 } ) \times (5- \frac{ 9 \sqrt{ 3 } }{ 2 } )=$$

Evaluate

$$\frac{131-75\sqrt{3}}{2}\approx 0.548094716$$

Short Solution Steps

To add or subtract expressions, expand them to make their denominators the same. Multiply 5 times \frac{2}{2}.

$$\left(5-3\sqrt{3}\right)\left(\frac{5\times 2}{2}-\frac{9\sqrt{3}}{2}\right)$$

Since \frac{5\times 2}{2} and \frac{9\sqrt{3}}{2} have the same denominator, subtract them by subtracting their numerators.

$$\left(5-3\sqrt{3}\right)\times \frac{5\times 2-9\sqrt{3}}{2}$$

Do the multiplications in 5\times 2-9\sqrt{3}.

$$\left(5-3\sqrt{3}\right)\times \frac{10-9\sqrt{3}}{2}$$

Express \left(5-3\sqrt{3}\right)\times \frac{10-9\sqrt{3}}{2} as a single fraction.

$$\frac{\left(5-3\sqrt{3}\right)\left(10-9\sqrt{3}\right)}{2}$$

Apply the distributive property by multiplying each term of 5-3\sqrt{3} by each term of 10-9\sqrt{3}.

$$\frac{50-45\sqrt{3}-30\sqrt{3}+27\left(\sqrt{3}\right)^{2}}{2}$$

Combine -45\sqrt{3} and -30\sqrt{3} to get -75\sqrt{3}.

$$\frac{50-75\sqrt{3}+27\left(\sqrt{3}\right)^{2}}{2}$$

The square of \sqrt{3} is 3.

$$\frac{50-75\sqrt{3}+27\times 3}{2}$$

Multiply 27 and 3 to get 81.

$$\frac{50-75\sqrt{3}+81}{2}$$

Add 50 and 81 to get 131.

$$\frac{131-75\sqrt{3}}{2}$$

Factor

$$\frac{131 - 75 \sqrt{3}}{2} = 0.5480947161670997$$