Solve frac{2sqrt{18}-sqrt{32}}{sqrt{8}+sqrt{2}}

$$\frac { 2 \sqrt { 18 } - \sqrt { 32 } } { \sqrt { 8 } + \sqrt { 2 } }$$

Evaluate

$$\frac{2}{3}\approx 0.666666667$$

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}.

$$\frac{2\times 3\sqrt{2}-\sqrt{32}}{\sqrt{8}+\sqrt{2}}$$

Multiply 2 and 3 to get 6.

$$\frac{6\sqrt{2}-\sqrt{32}}{\sqrt{8}+\sqrt{2}}$$

Factor 32=4^{2}\times 2. Rewrite the square root of the product \sqrt{4^{2}\times 2} as the product of square roots \sqrt{4^{2}}\sqrt{2}. Take the square root of 4^{2}.

$$\frac{6\sqrt{2}-4\sqrt{2}}{\sqrt{8}+\sqrt{2}}$$

Combine 6\sqrt{2} and -4\sqrt{2} to get 2\sqrt{2}.

$$\frac{2\sqrt{2}}{\sqrt{8}+\sqrt{2}}$$

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}.

$$\frac{2\sqrt{2}}{2\sqrt{2}+\sqrt{2}}$$

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

$$\frac{2\sqrt{2}}{3\sqrt{2}}$$

Cancel out \sqrt{2} in both numerator and denominator.

$$\frac{2}{3}$$

Factor

$$\frac{2}{3} = 0.6666666666666666$$