Solve (4-sqrt{3})(4-2sqrt{3})

$$( 4 - \sqrt { 3 } ) ( 4 - 2 \sqrt { 3 } )$$

Evaluate

$$22-12\sqrt{3}\approx 1.215390309$$

Solution Steps

Apply the distributive property by multiplying each term of 4-\sqrt{3} by each term of 4-2\sqrt{3}.

$$16-8\sqrt{3}-4\sqrt{3}+2\left(\sqrt{3}\right)^{2}$$

Combine -8\sqrt{3} and -4\sqrt{3} to get -12\sqrt{3}.

$$16-12\sqrt{3}+2\left(\sqrt{3}\right)^{2}$$

The square of \sqrt{3} is 3.

$$16-12\sqrt{3}+2\times 3$$

Multiply 2 and 3 to get 6.

$$16-12\sqrt{3}+6$$

Add 16 and 6 to get 22.

$$22-12\sqrt{3}$$

Factor

$$2 {(11 - 6 \sqrt{3})} = 1.215390309$$