Solve frac{1001+337/2sqrt{2}}{3sqrt{41}}

$$\frac { \frac { 1001 + 337 } { 2 \sqrt { 2 } } } { 3 \sqrt { 41 } }$$

Evaluate

$$\frac{223\sqrt{82}}{82}\approx 24.626230315$$

Solution Steps

Express \frac{\frac{1001+337}{2\sqrt{2}}}{3\sqrt{41}} as a single fraction.

$$\frac{1001+337}{2\sqrt{2}\times 3\sqrt{41}}$$

Add 1001 and 337 to get 1338.

$$\frac{1338}{2\sqrt{2}\times 3\sqrt{41}}$$

Multiply 2 and 3 to get 6.

$$\frac{1338}{6\sqrt{2}\sqrt{41}}$$

To multiply \sqrt{2} and \sqrt{41}, multiply the numbers under the square root.

$$\frac{1338}{6\sqrt{82}}$$

Rationalize the denominator of \frac{1338}{6\sqrt{82}} by multiplying numerator and denominator by \sqrt{82}.

$$\frac{1338\sqrt{82}}{6\left(\sqrt{82}\right)^{2}}$$

The square of \sqrt{82} is 82.

$$\frac{1338\sqrt{82}}{6\times 82}$$

Cancel out 6 in both numerator and denominator.

$$\frac{223\sqrt{82}}{82}$$