Solve frac{70+49sqrt{2}+190-98sqrt{2}+70+49sqrt{2}}{267+408}

$$\frac { 70 + 49 \sqrt { 2 } + 190 - 98 \sqrt { 2 } + 70 + 49 \sqrt { 2 } } { 267 + 408 }$$

Evaluate

$$\frac{22}{45}\approx 0.488888889$$

Solution Steps

Add 70 and 190 to get 260.

$$\frac{260+49\sqrt{2}-98\sqrt{2}+70+49\sqrt{2}}{267+408}$$

Combine 49\sqrt{2} and -98\sqrt{2} to get -49\sqrt{2}.

$$\frac{260-49\sqrt{2}+70+49\sqrt{2}}{267+408}$$

Add 260 and 70 to get 330.

$$\frac{330-49\sqrt{2}+49\sqrt{2}}{267+408}$$

Combine -49\sqrt{2} and 49\sqrt{2} to get 0.

$$\frac{330}{267+408}$$

Add 267 and 408 to get 675.

$$\frac{330}{675}$$

Reduce the fraction \frac{330}{675} to lowest terms by extracting and canceling out 15.

$$\frac{22}{45}$$

Factor

$$\frac{2 \cdot 11}{3 ^ {2} \cdot 5} = 0.4888888888888889$$