Solve (3sqrt{2}-sqrt{5})(sqrt{6}-sqrt{5})

$$( 3 \sqrt { 2 } - \sqrt { 5 } ) ( \sqrt { 6 } - \sqrt { 5 } )$$

Evaluate

$$6\sqrt{3}+5-\sqrt{30}-3\sqrt{10}\approx 0.42824629$$

Solution Steps

Apply the distributive property by multiplying each term of 3\sqrt{2}-\sqrt{5} by each term of \sqrt{6}-\sqrt{5}.

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

Factor 6=2\times 3. Rewrite the square root of the product \sqrt{2\times 3} as the product of square roots \sqrt{2}\sqrt{3}.

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

Multiply \sqrt{2} and \sqrt{2} to get 2.

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

Multiply 3 and 2 to get 6.

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

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

$$6\sqrt{3}-3\sqrt{10}-\sqrt{5}\sqrt{6}+\left(\sqrt{5}\right)^{2}$$

To multiply \sqrt{5} and \sqrt{6}, multiply the numbers under the square root.

$$6\sqrt{3}-3\sqrt{10}-\sqrt{30}+\left(\sqrt{5}\right)^{2}$$

The square of \sqrt{5} is 5.

$$6\sqrt{3}-3\sqrt{10}-\sqrt{30}+5$$