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

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

Evaluate

$$26-9\sqrt{6}\approx 3.954592315$$

Solution Steps

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

$$2\left(\sqrt{3}\right)^{2}-4\sqrt{3}\sqrt{2}-5\sqrt{2}\sqrt{3}+10\left(\sqrt{2}\right)^{2}$$

The square of \sqrt{3} is 3.

$$2\times 3-4\sqrt{3}\sqrt{2}-5\sqrt{2}\sqrt{3}+10\left(\sqrt{2}\right)^{2}$$

Multiply 2 and 3 to get 6.

$$6-4\sqrt{3}\sqrt{2}-5\sqrt{2}\sqrt{3}+10\left(\sqrt{2}\right)^{2}$$

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

$$6-4\sqrt{6}-5\sqrt{2}\sqrt{3}+10\left(\sqrt{2}\right)^{2}$$

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

$$6-4\sqrt{6}-5\sqrt{6}+10\left(\sqrt{2}\right)^{2}$$

Combine -4\sqrt{6} and -5\sqrt{6} to get -9\sqrt{6}.

$$6-9\sqrt{6}+10\left(\sqrt{2}\right)^{2}$$

The square of \sqrt{2} is 2.

$$6-9\sqrt{6}+10\times 2$$

Multiply 10 and 2 to get 20.

$$6-9\sqrt{6}+20$$

Add 6 and 20 to get 26.

$$26-9\sqrt{6}$$

Factor

$$26-9\sqrt{6}$$