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

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

Evaluate

$$14\sqrt{6}+21\sqrt{10}-2\sqrt{15}-15\approx 77.95472057$$

Solution Steps

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

$$21\sqrt{5}\sqrt{2}-3\left(\sqrt{5}\right)^{2}+14\sqrt{3}\sqrt{2}-2\sqrt{3}\sqrt{5}$$

To multiply \sqrt{5} and \sqrt{2}, multiply the numbers under the square root.

$$21\sqrt{10}-3\left(\sqrt{5}\right)^{2}+14\sqrt{3}\sqrt{2}-2\sqrt{3}\sqrt{5}$$

The square of \sqrt{5} is 5.

$$21\sqrt{10}-3\times 5+14\sqrt{3}\sqrt{2}-2\sqrt{3}\sqrt{5}$$

Multiply -3 and 5 to get -15.

$$21\sqrt{10}-15+14\sqrt{3}\sqrt{2}-2\sqrt{3}\sqrt{5}$$

To multiply \sqrt{3} and \sqrt{2}, multiply the numbers under the square root.

$$21\sqrt{10}-15+14\sqrt{6}-2\sqrt{3}\sqrt{5}$$

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

$$21\sqrt{10}-15+14\sqrt{6}-2\sqrt{15}$$

Factor

$$14 \sqrt{6} + 21 \sqrt{10} - 2 \sqrt{15} - 15 = 77.95472057$$