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

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

Evaluate

$$\sqrt{2}-2\approx -0.585786438$$

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}.

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

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

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

The square of \sqrt{2} is 2.

$$2\times 2+4\sqrt{2}-3\sqrt{2}-6$$

Multiply 2 and 2 to get 4.

$$4+4\sqrt{2}-3\sqrt{2}-6$$

Combine 4\sqrt{2} and -3\sqrt{2} to get \sqrt{2}.

$$4+\sqrt{2}-6$$

Subtract 6 from 4 to get -2.

$$-2+\sqrt{2}$$

Factor

$$\sqrt{2} - 2 = -0.585786438$$