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

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

Evaluate

$$2\sqrt{6}+6-\sqrt{10}-\sqrt{15}\approx 3.863718479$$

Solution Steps

Use the distributive property to multiply 1 by 2\sqrt{3}-\sqrt{5}.

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

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

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

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

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

The square of \sqrt{3} is 3.

$$2\sqrt{6}+2\times 3-\sqrt{5}\sqrt{2}-\sqrt{5}\sqrt{3}$$

Multiply 2 and 3 to get 6.

$$2\sqrt{6}+6-\sqrt{5}\sqrt{2}-\sqrt{5}\sqrt{3}$$

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

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

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

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