Solve {l}{sqrt{8}-sqrt{18}}{+sqrt{7}}

$$\left. \begin{array} { l } { \sqrt { 8 } - \sqrt { 18 } } \\ { + \sqrt { 7 } } \end{array} \right.$$

Evaluate

$$\sqrt{7}-\sqrt{2}\approx 1.231537749$$

Solution Steps

Factor 8=2^{2}\times 2. Rewrite the square root of the product \sqrt{2^{2}\times 2} as the product of square roots \sqrt{2^{2}}\sqrt{2}. Take the square root of 2^{2}.

$$2\sqrt{2}-\sqrt{18}+\sqrt{7}$$

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}.

$$2\sqrt{2}-3\sqrt{2}+\sqrt{7}$$

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

$$-\sqrt{2}+\sqrt{7}$$