Solve 100/sqrt{2}7*3/sqrt{2}cos(43.3)

$$\frac{ 100 }{ \sqrt{ 2 } } \frac{ 7 \cdot 3 }{ \sqrt{ 2 } } \cos ( 43.3 )$$

Evaluate

$$764.161395540071025$$

Solution Steps

Evaluate trigonometric functions in the problem

$$\frac{100}{\sqrt{2}} \frac{7 \cdot 3}{\sqrt{2}} 0.7277727576572105$$

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

$$0.7277727576572105\times \frac{100\sqrt{2}}{\left(\sqrt{2}\right)^{2}}\times \frac{7\times 3}{\sqrt{2}}$$

The square of \sqrt{2} is 2.

$$0.7277727576572105\times \frac{100\sqrt{2}}{2}\times \frac{7\times 3}{\sqrt{2}}$$

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

$$0.7277727576572105\times 50\sqrt{2}\times \frac{7\times 3}{\sqrt{2}}$$

Multiply 0.7277727576572105 and 50 to get 36.388637882860525.

$$36.388637882860525\sqrt{2}\times \frac{7\times 3}{\sqrt{2}}$$

Multiply 7 and 3 to get 21.

$$36.388637882860525\sqrt{2}\times \frac{21}{\sqrt{2}}$$

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

$$36.388637882860525\sqrt{2}\times \frac{21\sqrt{2}}{\left(\sqrt{2}\right)^{2}}$$

The square of \sqrt{2} is 2.

$$36.388637882860525\sqrt{2}\times \frac{21\sqrt{2}}{2}$$

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

$$36.388637882860525\times \frac{\sqrt{2}\times 21\sqrt{2}}{2}$$

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

$$36.388637882860525\times \frac{2\times 21}{2}$$

Cancel out 2 and 2.

$$36.388637882860525\times 21$$

Multiply 36.388637882860525 and 21 to get 764.161395540071025.

$$764.161395540071025$$

Factor

$$\frac{3 \cdot 7 \cdot 19 \cdot 76607658700759}{2 ^ {15} \cdot 5 ^ {13}} = 764\frac{6455821602840}{40000000000000} = 764.161395540071$$