Solve 6/7+5/sqrt{8}*9=

$$\frac { 6 } { 7 } + \frac { 5 } { \sqrt { 8 } } \times 9 =$$

Evaluate

$$\frac{45\sqrt{2}}{4}+\frac{6}{7}\approx 16.767045434$$

Short 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}.

$$\frac{6}{7}+9\times \frac{5}{2\sqrt{2}}$$

Rationalize the denominator of \frac{5}{2\sqrt{2}} by multiplying numerator and denominator by \sqrt{2}.

$$\frac{6}{7}+9\times \frac{5\sqrt{2}}{2\left(\sqrt{2}\right)^{2}}$$

The square of \sqrt{2} is 2.

$$\frac{6}{7}+9\times \frac{5\sqrt{2}}{2\times 2}$$

Multiply 2 and 2 to get 4.

$$\frac{6}{7}+9\times \frac{5\sqrt{2}}{4}$$

Express 9\times \frac{5\sqrt{2}}{4} as a single fraction.

$$\frac{6}{7}+\frac{9\times 5\sqrt{2}}{4}$$

To add or subtract expressions, expand them to make their denominators the same. Least common multiple of 7 and 4 is 28. Multiply \frac{6}{7} times \frac{4}{4}. Multiply \frac{9\times 5\sqrt{2}}{4} times \frac{7}{7}.

$$\frac{6\times 4}{28}+\frac{7\times 9\times 5\sqrt{2}}{28}$$

Since \frac{6\times 4}{28} and \frac{7\times 9\times 5\sqrt{2}}{28} have the same denominator, add them by adding their numerators.

$$\frac{6\times 4+7\times 9\times 5\sqrt{2}}{28}$$

Do the multiplications in 6\times 4+7\times 9\times 5\sqrt{2}.

$$\frac{24+315\sqrt{2}}{28}$$

Factor

$$\frac{3 {(105 \sqrt{2} + 8)}}{28} = 16.767045433840178$$