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

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

Evaluate

$$18-6\sqrt{6}\approx 3.303061543$$

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}.

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

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

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

Use the distributive property to multiply 3\sqrt{2}-2\sqrt{3} by 3.

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

Use the distributive property to multiply 9\sqrt{2}-6\sqrt{3} by \sqrt{2}.

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

The square of \sqrt{2} is 2.

$$9\times 2-6\sqrt{3}\sqrt{2}$$

Multiply 9 and 2 to get 18.

$$18-6\sqrt{3}\sqrt{2}$$

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

$$18-6\sqrt{6}$$

Factor

$$6 {(3 - \sqrt{6})} = 3.303061543$$