Solve sqrt{2*(1+cos(2*9.4)/2)/sin(2*20)}

$$\sqrt{ \frac{ 2 \times ( \frac{ 1+ \cos ( 2 \times 9.4 ) }{ 2 } ) }{ \sin ( 2 \times 20 ) } }$$

Evaluate

$$\frac{2\sqrt{31282050620195969317781393136713}}{6427876096865393}\approx 1.740243844$$

Solution Steps

Evaluate trigonometric functions in the problem

$$\sqrt{\frac{2 \cdot {(\frac{1 + 0.9466492601156964}{2})}}{0.6427876096865393}}$$

Add 1 and 0.9466492601156964 to get 1.9466492601156964.

$$\sqrt{\frac{2\times \frac{1.9466492601156964}{2}}{0.6427876096865393}}$$

Expand \frac{1.9466492601156964}{2} by multiplying both numerator and the denominator by 10000000000000000.

$$\sqrt{\frac{2\times \frac{19466492601156964}{20000000000000000}}{0.6427876096865393}}$$

Reduce the fraction \frac{19466492601156964}{20000000000000000} to lowest terms by extracting and canceling out 4.

$$\sqrt{\frac{2\times \frac{4866623150289241}{5000000000000000}}{0.6427876096865393}}$$

Express 2\times \frac{4866623150289241}{5000000000000000} as a single fraction.

$$\sqrt{\frac{\frac{2\times 4866623150289241}{5000000000000000}}{0.6427876096865393}}$$

Multiply 2 and 4866623150289241 to get 9733246300578482.

$$\sqrt{\frac{\frac{9733246300578482}{5000000000000000}}{0.6427876096865393}}$$

Reduce the fraction \frac{9733246300578482}{5000000000000000} to lowest terms by extracting and canceling out 2.

$$\sqrt{\frac{\frac{4866623150289241}{2500000000000000}}{0.6427876096865393}}$$

Express \frac{\frac{4866623150289241}{2500000000000000}}{0.6427876096865393} as a single fraction.

$$\sqrt{\frac{4866623150289241}{2500000000000000\times 0.6427876096865393}}$$

Multiply 2500000000000000 and 0.6427876096865393 to get 1606969024216348.25.

$$\sqrt{\frac{4866623150289241}{1606969024216348.25}}$$

Expand \frac{4866623150289241}{1606969024216348.25} by multiplying both numerator and the denominator by 100.

$$\sqrt{\frac{486662315028924100}{160696902421634825}}$$

Reduce the fraction \frac{486662315028924100}{160696902421634825} to lowest terms by extracting and canceling out 25.

$$\sqrt{\frac{19466492601156964}{6427876096865393}}$$

Rewrite the square root of the division \sqrt{\frac{19466492601156964}{6427876096865393}} as the division of square roots \frac{\sqrt{19466492601156964}}{\sqrt{6427876096865393}}.

$$\frac{\sqrt{19466492601156964}}{\sqrt{6427876096865393}}$$

Factor 19466492601156964=2^{2}\times 4866623150289241. Rewrite the square root of the product \sqrt{2^{2}\times 4866623150289241} as the product of square roots \sqrt{2^{2}}\sqrt{4866623150289241}. Take the square root of 2^{2}.

$$\frac{2\sqrt{4866623150289241}}{\sqrt{6427876096865393}}$$

Rationalize the denominator of \frac{2\sqrt{4866623150289241}}{\sqrt{6427876096865393}} by multiplying numerator and denominator by \sqrt{6427876096865393}.

$$\frac{2\sqrt{4866623150289241}\sqrt{6427876096865393}}{\left(\sqrt{6427876096865393}\right)^{2}}$$

The square of \sqrt{6427876096865393} is 6427876096865393.

$$\frac{2\sqrt{4866623150289241}\sqrt{6427876096865393}}{6427876096865393}$$

To multiply \sqrt{4866623150289241} and \sqrt{6427876096865393}, multiply the numbers under the square root.

$$\frac{2\sqrt{31282050620195969317781393136713}}{6427876096865393}$$