Solve (3sqrt{2}+1)(sqrt{8}-2)

$$(3 \sqrt{ 2 } +1)( \sqrt{ 8 } -2)$$

Evaluate

$$10-4\sqrt{2}\approx 4.343145751$$

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}.

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

Apply the distributive property by multiplying each term of 3\sqrt{2}+1 by each term of 2\sqrt{2}-2.

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

The square of \sqrt{2} is 2.

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

Multiply 6 and 2 to get 12.

$$12-6\sqrt{2}+2\sqrt{2}-2$$

Combine -6\sqrt{2} and 2\sqrt{2} to get -4\sqrt{2}.

$$12-4\sqrt{2}-2$$

Subtract 2 from 12 to get 10.

$$10-4\sqrt{2}$$