Solve (4+5sqrt{3})(4-sqrt{3})

$$( 4 + 5 \sqrt { 3 } ) ( 4 - \sqrt { 3 } )$$

Evaluate

$$16\sqrt{3}+1\approx 28.712812921$$

Solution Steps

Apply the distributive property by multiplying each term of 4+5\sqrt{3} by each term of 4-\sqrt{3}.

$$16-4\sqrt{3}+20\sqrt{3}-5\left(\sqrt{3}\right)^{2}$$

Combine -4\sqrt{3} and 20\sqrt{3} to get 16\sqrt{3}.

$$16+16\sqrt{3}-5\left(\sqrt{3}\right)^{2}$$

The square of \sqrt{3} is 3.

$$16+16\sqrt{3}-5\times 3$$

Multiply -5 and 3 to get -15.

$$16+16\sqrt{3}-15$$

Subtract 15 from 16 to get 1.

$$1+16\sqrt{3}$$