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

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

Evaluate

$$11\sqrt{3}-17\approx 2.052558883$$

Solution Steps

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

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

The square of \sqrt{3} is 3.

$$10\sqrt{3}-2-5\times 3+\sqrt{3}$$

Multiply -5 and 3 to get -15.

$$10\sqrt{3}-2-15+\sqrt{3}$$

Subtract 15 from -2 to get -17.

$$10\sqrt{3}-17+\sqrt{3}$$

Combine 10\sqrt{3} and \sqrt{3} to get 11\sqrt{3}.

$$11\sqrt{3}-17$$