Solve (2*sqrt{50}-sqrt{18})*sqrt{2}=

$$( 2 \cdot \sqrt { 50 } - \sqrt { 18 } ) \cdot \sqrt { 2 } =$$

Evaluate

$$14$$

Solution Steps

Factor 50=5^{2}\times 2. Rewrite the square root of the product \sqrt{5^{2}\times 2} as the product of square roots \sqrt{5^{2}}\sqrt{2}. Take the square root of 5^{2}.

$$\left(2\times 5\sqrt{2}-\sqrt{18}\right)\sqrt{2}$$

Multiply 2 and 5 to get 10.

$$\left(10\sqrt{2}-\sqrt{18}\right)\sqrt{2}$$

Factor 18=3^{2}\times 2. Rewrite the square root of the product \sqrt{3^{2}\times 2} as the product of square roots \sqrt{3^{2}}\sqrt{2}. Take the square root of 3^{2}.

$$\left(10\sqrt{2}-3\sqrt{2}\right)\sqrt{2}$$

Combine 10\sqrt{2} and -3\sqrt{2} to get 7\sqrt{2}.

$$7\sqrt{2}\sqrt{2}$$

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

$$7\times 2$$

Multiply 7 and 2 to get 14.

$$14$$

Factor

$$2\times 7$$