Solve (-2sqrt{5}-4sqrt{11})(5sqrt{5}-4sqrt{11})

$$( - 2 \sqrt { 5 } - 4 \sqrt { 11 } ) ( 5 \sqrt { 5 } - 4 \sqrt { 11 } )$$

Evaluate

$$126-12\sqrt{55}\approx 37.005618155$$

Solution Steps

Apply the distributive property by multiplying each term of -2\sqrt{5}-4\sqrt{11} by each term of 5\sqrt{5}-4\sqrt{11}.

$$-10\left(\sqrt{5}\right)^{2}+8\sqrt{11}\sqrt{5}-20\sqrt{11}\sqrt{5}+16\left(\sqrt{11}\right)^{2}$$

The square of \sqrt{5} is 5.

$$-10\times 5+8\sqrt{11}\sqrt{5}-20\sqrt{11}\sqrt{5}+16\left(\sqrt{11}\right)^{2}$$

Multiply -10 and 5 to get -50.

$$-50+8\sqrt{11}\sqrt{5}-20\sqrt{11}\sqrt{5}+16\left(\sqrt{11}\right)^{2}$$

To multiply \sqrt{11} and \sqrt{5}, multiply the numbers under the square root.

$$-50+8\sqrt{55}-20\sqrt{11}\sqrt{5}+16\left(\sqrt{11}\right)^{2}$$

To multiply \sqrt{11} and \sqrt{5}, multiply the numbers under the square root.

$$-50+8\sqrt{55}-20\sqrt{55}+16\left(\sqrt{11}\right)^{2}$$

Combine 8\sqrt{55} and -20\sqrt{55} to get -12\sqrt{55}.

$$-50-12\sqrt{55}+16\left(\sqrt{11}\right)^{2}$$

The square of \sqrt{11} is 11.

$$-50-12\sqrt{55}+16\times 11$$

Multiply 16 and 11 to get 176.

$$-50-12\sqrt{55}+176$$

Add -50 and 176 to get 126.

$$126-12\sqrt{55}$$

Factor

$$6 {(21 - 2 \sqrt{55})} = 37.005618155$$