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

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

Evaluate

$$4-13\sqrt{2}\approx -14.384776311$$

Solution Steps

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

$$10-15\sqrt{2}+2\sqrt{2}-3\left(\sqrt{2}\right)^{2}$$

Combine -15\sqrt{2} and 2\sqrt{2} to get -13\sqrt{2}.

$$10-13\sqrt{2}-3\left(\sqrt{2}\right)^{2}$$

The square of \sqrt{2} is 2.

$$10-13\sqrt{2}-3\times 2$$

Multiply -3 and 2 to get -6.

$$10-13\sqrt{2}-6$$

Subtract 6 from 10 to get 4.

$$4-13\sqrt{2}$$

Factor

$$4-13\sqrt{2}$$