Solve frac{8+9+sqrt{2}}{10}*sqrt{8}

$$\frac { 8 + 9 + \sqrt { 2 } } { 10 } \times \sqrt { 8 }$$

Evaluate

$$\frac{17\sqrt{2}+2}{5}\approx 5.208326112$$

Solution Steps

Add 8 and 9 to get 17.

$$\frac{17+\sqrt{2}}{10}\sqrt{8}$$

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}.

$$\frac{17+\sqrt{2}}{10}\times 2\sqrt{2}$$

Cancel out 10, the greatest common factor in 2 and 10.

$$\frac{17+\sqrt{2}}{5}\sqrt{2}$$

Express \frac{17+\sqrt{2}}{5}\sqrt{2} as a single fraction.

$$\frac{\left(17+\sqrt{2}\right)\sqrt{2}}{5}$$

Use the distributive property to multiply 17+\sqrt{2} by \sqrt{2}.

$$\frac{17\sqrt{2}+\left(\sqrt{2}\right)^{2}}{5}$$

The square of \sqrt{2} is 2.

$$\frac{17\sqrt{2}+2}{5}$$