Solve (7-5sqrt{3})*(2-8sqrt{3})

$$( 7 - 5 \sqrt { 3 } ) \cdot ( 2 - 8 \sqrt { 3 } )$$

Evaluate

$$134-66\sqrt{3}\approx 19.6846467$$

Solution Steps

Apply the distributive property by multiplying each term of 7-5\sqrt{3} by each term of 2-8\sqrt{3}.

$$14-56\sqrt{3}-10\sqrt{3}+40\left(\sqrt{3}\right)^{2}$$

Combine -56\sqrt{3} and -10\sqrt{3} to get -66\sqrt{3}.

$$14-66\sqrt{3}+40\left(\sqrt{3}\right)^{2}$$

The square of \sqrt{3} is 3.

$$14-66\sqrt{3}+40\times 3$$

Multiply 40 and 3 to get 120.

$$14-66\sqrt{3}+120$$

Add 14 and 120 to get 134.

$$134-66\sqrt{3}$$

Factor

$$2 {(67 - 33 \sqrt{3})} = 19.6846467$$