Solve (sqrt{82}-sqrt{2})*sqrt{2}

$$( \sqrt { 82 } - \sqrt { 2 } ) \cdot \sqrt { 2 }$$

Evaluate

$$2\left(\sqrt{41}-1\right)\approx 10.806248475$$

Solution Steps

Use the distributive property to multiply \sqrt{82}-\sqrt{2} by \sqrt{2}.

$$\sqrt{82}\sqrt{2}-\left(\sqrt{2}\right)^{2}$$

Factor 82=2\times 41. Rewrite the square root of the product \sqrt{2\times 41} as the product of square roots \sqrt{2}\sqrt{41}.

$$\sqrt{2}\sqrt{41}\sqrt{2}-\left(\sqrt{2}\right)^{2}$$

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

$$2\sqrt{41}-\left(\sqrt{2}\right)^{2}$$

The square of \sqrt{2} is 2.

$$2\sqrt{41}-2$$