Solve (5sqrt{3}+3)(2sqrt{3}-1)

$$( 5 \sqrt { 3 } + 3 ) ( 2 \sqrt { 3 } - 1 )$$

Evaluate

$$\sqrt{3}+27\approx 28.732050808$$

Solution Steps

Apply the distributive property by multiplying each term of 5\sqrt{3}+3 by each term of 2\sqrt{3}-1.

$$10\left(\sqrt{3}\right)^{2}-5\sqrt{3}+6\sqrt{3}-3$$

The square of \sqrt{3} is 3.

$$10\times 3-5\sqrt{3}+6\sqrt{3}-3$$

Multiply 10 and 3 to get 30.

$$30-5\sqrt{3}+6\sqrt{3}-3$$

Combine -5\sqrt{3} and 6\sqrt{3} to get \sqrt{3}.

$$30+\sqrt{3}-3$$

Subtract 3 from 30 to get 27.

$$27+\sqrt{3}$$

Factor

$$\sqrt{3} + 27 = 28.732050808$$