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

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

Evaluate

$$-\sqrt{15}-1\approx -4.872983346$$

Solution Steps

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

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

The square of \sqrt{5} is 5.

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

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

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

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

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

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

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

The square of \sqrt{3} is 3.

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

Multiply -2 and 3 to get -6.

$$5-\sqrt{15}-6$$

Subtract 6 from 5 to get -1.

$$-1-\sqrt{15}$$