Solve 100/sqrt{2}7*3/sqrt{2}cos(433)

$$\frac{ 100 }{ \sqrt{ 2 } } \frac{ 7 \cdot 3 }{ \sqrt{ 2 } } \cos ( 433 )$$

Evaluate

$$306.990289958873115$$

Solution Steps

Evaluate trigonometric functions in the problem

$$\frac{100}{\sqrt{2}} \frac{7 \cdot 3}{\sqrt{2}} 0.2923717047227363$$

Rationalize the denominator of \frac{100}{\sqrt{2}} by multiplying numerator and denominator by \sqrt{2}.

$$0.2923717047227363\times \frac{100\sqrt{2}}{\left(\sqrt{2}\right)^{2}}\times \frac{7\times 3}{\sqrt{2}}$$

The square of \sqrt{2} is 2.

$$0.2923717047227363\times \frac{100\sqrt{2}}{2}\times \frac{7\times 3}{\sqrt{2}}$$

Divide 100\sqrt{2} by 2 to get 50\sqrt{2}.

$$0.2923717047227363\times 50\sqrt{2}\times \frac{7\times 3}{\sqrt{2}}$$

Multiply 0.2923717047227363 and 50 to get 14.618585236136815.

$$14.618585236136815\sqrt{2}\times \frac{7\times 3}{\sqrt{2}}$$

Multiply 7 and 3 to get 21.

$$14.618585236136815\sqrt{2}\times \frac{21}{\sqrt{2}}$$

Rationalize the denominator of \frac{21}{\sqrt{2}} by multiplying numerator and denominator by \sqrt{2}.

$$14.618585236136815\sqrt{2}\times \frac{21\sqrt{2}}{\left(\sqrt{2}\right)^{2}}$$

The square of \sqrt{2} is 2.

$$14.618585236136815\sqrt{2}\times \frac{21\sqrt{2}}{2}$$

Express \sqrt{2}\times \frac{21\sqrt{2}}{2} as a single fraction.

$$14.618585236136815\times \frac{\sqrt{2}\times 21\sqrt{2}}{2}$$

Multiply \sqrt{2} and \sqrt{2} to get 2.

$$14.618585236136815\times \frac{2\times 21}{2}$$

Cancel out 2 and 2.

$$14.618585236136815\times 21$$

Multiply 14.618585236136815 and 21 to get 306.990289958873115.

$$306.990289958873115$$

Factor

$$\frac{3 \cdot 7 \cdot 373 \cdot 25679 \cdot 305244889}{2 ^ {15} \cdot 5 ^ {14}} = 306\frac{198057991774624}{200000000000000} = 306.9902899588731$$