Solve (sqrt{18}+sqrt{2})*5sqrt{2}

$$( \sqrt { 18 } + \sqrt { 2 } ) \times 5 \sqrt { 2 }$$

Evaluate

$$40$$

Solution Steps

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}.

$$5\left(3\sqrt{2}+\sqrt{2}\right)\sqrt{2}$$

Combine 3\sqrt{2} and \sqrt{2} to get 4\sqrt{2}.

$$5\times 4\sqrt{2}\sqrt{2}$$

Multiply 5 and 4 to get 20.

$$20\sqrt{2}\sqrt{2}$$

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

$$20\times 2$$

Multiply 20 and 2 to get 40.

$$40$$

Factor

$$2^{3}\times 5$$