Solve (sqrt{98}-5sqrt{2})*sqrt{2}

$$( \sqrt { 98 } - 5 \sqrt { 2 } ) \cdot \sqrt { 2 }$$

Evaluate

$$4$$

Solution Steps

Factor 98=7^{2}\times 2. Rewrite the square root of the product \sqrt{7^{2}\times 2} as the product of square roots \sqrt{7^{2}}\sqrt{2}. Take the square root of 7^{2}.

$$\left(7\sqrt{2}-5\sqrt{2}\right)\sqrt{2}$$

Combine 7\sqrt{2} and -5\sqrt{2} to get 2\sqrt{2}.

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

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

$$2\times 2$$

Multiply 2 and 2 to get 4.

$$4$$

Factor

$$2^{2}$$