Solve (3-sqrt{8})(3+sqrt{2})

$$( 3 - \sqrt { 8 } ) ( 3 + \sqrt { 2 } )$$

Evaluate

$$5-3\sqrt{2}\approx 0.757359313$$

Solution Steps

Factor 8=2^{2}\times 2. Rewrite the square root of the product \sqrt{2^{2}\times 2} as the product of square roots \sqrt{2^{2}}\sqrt{2}. Take the square root of 2^{2}.

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

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

$$9+3\sqrt{2}-6\sqrt{2}-2\left(\sqrt{2}\right)^{2}$$

Combine 3\sqrt{2} and -6\sqrt{2} to get -3\sqrt{2}.

$$9-3\sqrt{2}-2\left(\sqrt{2}\right)^{2}$$

The square of \sqrt{2} is 2.

$$9-3\sqrt{2}-2\times 2$$

Multiply -2 and 2 to get -4.

$$9-3\sqrt{2}-4$$

Subtract 4 from 9 to get 5.

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