Solve (sqrt{5}+4sqrt{3})(sqrt{5}-2sqrt{3})

$$( \sqrt { 5 } + 4 \sqrt { 3 } ) ( \sqrt { 5 } - 2 \sqrt { 3 } )$$

Evaluate

$$2\sqrt{15}-19\approx -11.254033308$$

Solution Steps

Apply the distributive property by multiplying each term of \sqrt{5}+4\sqrt{3} by each term of \sqrt{5}-2\sqrt{3}.

$$\left(\sqrt{5}\right)^{2}-2\sqrt{5}\sqrt{3}+4\sqrt{3}\sqrt{5}-8\left(\sqrt{3}\right)^{2}$$

The square of \sqrt{5} is 5.

$$5-2\sqrt{5}\sqrt{3}+4\sqrt{3}\sqrt{5}-8\left(\sqrt{3}\right)^{2}$$

To multiply \sqrt{5} and \sqrt{3}, multiply the numbers under the square root.

$$5-2\sqrt{15}+4\sqrt{3}\sqrt{5}-8\left(\sqrt{3}\right)^{2}$$

To multiply \sqrt{3} and \sqrt{5}, multiply the numbers under the square root.

$$5-2\sqrt{15}+4\sqrt{15}-8\left(\sqrt{3}\right)^{2}$$

Combine -2\sqrt{15} and 4\sqrt{15} to get 2\sqrt{15}.

$$5+2\sqrt{15}-8\left(\sqrt{3}\right)^{2}$$

The square of \sqrt{3} is 3.

$$5+2\sqrt{15}-8\times 3$$

Multiply -8 and 3 to get -24.

$$5+2\sqrt{15}-24$$

Subtract 24 from 5 to get -19.

$$-19+2\sqrt{15}$$