Solve (1sqrt{7}-2sqrt{5})(3sqrt{5}+2sqrt{7})

$$( 1 \sqrt { 7 } - 2 \sqrt { 5 } ) ( 3 \sqrt { 5 } + 2 \sqrt { 7 } )$$

Evaluate

$$-\sqrt{35}-16\approx -21.916079783$$

Solution Steps

Apply the distributive property by multiplying each term of 1\sqrt{7}-2\sqrt{5} by each term of 3\sqrt{5}+2\sqrt{7}.

$$3\sqrt{7}\sqrt{5}+2\left(\sqrt{7}\right)^{2}-6\left(\sqrt{5}\right)^{2}-4\sqrt{5}\sqrt{7}$$

To multiply \sqrt{7} and \sqrt{5}, multiply the numbers under the square root.

$$3\sqrt{35}+2\left(\sqrt{7}\right)^{2}-6\left(\sqrt{5}\right)^{2}-4\sqrt{5}\sqrt{7}$$

The square of \sqrt{7} is 7.

$$3\sqrt{35}+2\times 7-6\left(\sqrt{5}\right)^{2}-4\sqrt{5}\sqrt{7}$$

Multiply 2 and 7 to get 14.

$$3\sqrt{35}+14-6\left(\sqrt{5}\right)^{2}-4\sqrt{5}\sqrt{7}$$

The square of \sqrt{5} is 5.

$$3\sqrt{35}+14-6\times 5-4\sqrt{5}\sqrt{7}$$

Multiply -6 and 5 to get -30.

$$3\sqrt{35}+14-30-4\sqrt{5}\sqrt{7}$$

Subtract 30 from 14 to get -16.

$$3\sqrt{35}-16-4\sqrt{5}\sqrt{7}$$

To multiply \sqrt{5} and \sqrt{7}, multiply the numbers under the square root.

$$3\sqrt{35}-16-4\sqrt{35}$$

Combine 3\sqrt{35} and -4\sqrt{35} to get -\sqrt{35}.

$$-\sqrt{35}-16$$