Solve (5-sqrt{3})(3+2sqrt{3})

$$( 5 - \sqrt { 3 } ) ( 3 + 2 \sqrt { 3 } )$$

Evaluate

$$7\sqrt{3}+9\approx 21.124355653$$

Solution Steps

Apply the distributive property by multiplying each term of 5-\sqrt{3} by each term of 3+2\sqrt{3}.

$$15+10\sqrt{3}-3\sqrt{3}-2\left(\sqrt{3}\right)^{2}$$

Combine 10\sqrt{3} and -3\sqrt{3} to get 7\sqrt{3}.

$$15+7\sqrt{3}-2\left(\sqrt{3}\right)^{2}$$

The square of \sqrt{3} is 3.

$$15+7\sqrt{3}-2\times 3$$

Multiply -2 and 3 to get -6.

$$15+7\sqrt{3}-6$$

Subtract 6 from 15 to get 9.

$$9+7\sqrt{3}$$

Factor

$$7 \sqrt{3} + 9 = 21.124355653$$