Solve {l}{4sqrt{2}+sqrt{50}-}{-sqrt{18}}

$$\left. \begin{array} { l } { 4 \sqrt { 2 } + \sqrt { 50 } - } \\ { - \sqrt { 18 } } \end{array} \right.$$

Evaluate

$$12\sqrt{2}\approx 16.970562748$$

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}.

$$4\sqrt{2}+5\sqrt{2}-\left(-\sqrt{18}\right)$$

Combine 4\sqrt{2} and 5\sqrt{2} to get 9\sqrt{2}.

$$9\sqrt{2}-\left(-\sqrt{18}\right)$$

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}.

$$9\sqrt{2}-\left(-3\sqrt{2}\right)$$

Multiply -1 and -1 to get 1.

$$9\sqrt{2}+3\sqrt{2}$$

Combine 9\sqrt{2} and 3\sqrt{2} to get 12\sqrt{2}.

$$12\sqrt{2}$$