Solve (sqrt{10}-sqrt{6})(sqrt{2}+1)

$$( \sqrt { 10 } - \sqrt { 6 } ) ( \sqrt { 2 } + 1 )$$

Evaluate

$$\sqrt{10}+2\sqrt{5}-\sqrt{6}-2\sqrt{3}\approx 1.720822257$$

Solution Steps

Apply the distributive property by multiplying each term of \sqrt{10}-\sqrt{6} by each term of \sqrt{2}+1.

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

Factor 10=2\times 5. Rewrite the square root of the product \sqrt{2\times 5} as the product of square roots \sqrt{2}\sqrt{5}.

$$\sqrt{2}\sqrt{5}\sqrt{2}+\sqrt{10}-\sqrt{6}\sqrt{2}-\sqrt{6}$$

Multiply \sqrt{2} and \sqrt{2} to get 2.

$$2\sqrt{5}+\sqrt{10}-\sqrt{6}\sqrt{2}-\sqrt{6}$$

Factor 6=2\times 3. Rewrite the square root of the product \sqrt{2\times 3} as the product of square roots \sqrt{2}\sqrt{3}.

$$2\sqrt{5}+\sqrt{10}-\sqrt{2}\sqrt{3}\sqrt{2}-\sqrt{6}$$

Multiply \sqrt{2} and \sqrt{2} to get 2.

$$2\sqrt{5}+\sqrt{10}-2\sqrt{3}-\sqrt{6}$$