Solve 1.44^2*3.142/4*1.5*6.022*(cotpi/12)^2*(0.7*79^2/197+0.3*49^2/108)

$$1.44 ^ { 2 } \times \frac { 3.142 } { 4 } \times 1.5 \times 6.022 \times ( \cot \frac { \pi } { 12 } ) ^ { 2 } \times ( 0.7 \times \frac { 79 ^ { 2 } } { 197 } + 0.3 \times \frac { 49 ^ { 2 } } { 108 } )$$

Evaluate

$$\frac{5686092592904255006623643174117092700760081507}{961914062500000000000000000000000000000000}\approx 5911.227223486$$

Solution Steps

Evaluate trigonometric functions in the problem

$$1.44 ^ {2} \cdot \frac{3.142}{4} \cdot 1.5 \cdot 6.022 \cdot 3.7320508075688776 ^ {2} \cdot {(0.7 \cdot \frac{79 ^ {2}}{197} + 0.3 \cdot \frac{49 ^ {2}}{108})}$$

Calculate 1.44 to the power of 2 and get 2.0736.

$$2.0736\times \frac{3.142}{4}\times 1.5\times 6.022\times 3.7320508075688776^{2}\left(0.7\times \frac{79^{2}}{197}+0.3\times \frac{49^{2}}{108}\right)$$

Expand \frac{3.142}{4} by multiplying both numerator and the denominator by 1000.

$$2.0736\times \frac{3142}{4000}\times 1.5\times 6.022\times 3.7320508075688776^{2}\left(0.7\times \frac{79^{2}}{197}+0.3\times \frac{49^{2}}{108}\right)$$

Reduce the fraction \frac{3142}{4000} to lowest terms by extracting and canceling out 2.

$$2.0736\times \frac{1571}{2000}\times 1.5\times 6.022\times 3.7320508075688776^{2}\left(0.7\times \frac{79^{2}}{197}+0.3\times \frac{49^{2}}{108}\right)$$

Convert decimal number 2.0736 to fraction \frac{20736}{10000}. Reduce the fraction \frac{20736}{10000} to lowest terms by extracting and canceling out 16.

$$\frac{1296}{625}\times \frac{1571}{2000}\times 1.5\times 6.022\times 3.7320508075688776^{2}\left(0.7\times \frac{79^{2}}{197}+0.3\times \frac{49^{2}}{108}\right)$$

Multiply \frac{1296}{625} times \frac{1571}{2000} by multiplying numerator times numerator and denominator times denominator.

$$\frac{1296\times 1571}{625\times 2000}\times 1.5\times 6.022\times 3.7320508075688776^{2}\left(0.7\times \frac{79^{2}}{197}+0.3\times \frac{49^{2}}{108}\right)$$

Do the multiplications in the fraction \frac{1296\times 1571}{625\times 2000}.

$$\frac{2036016}{1250000}\times 1.5\times 6.022\times 3.7320508075688776^{2}\left(0.7\times \frac{79^{2}}{197}+0.3\times \frac{49^{2}}{108}\right)$$

Reduce the fraction \frac{2036016}{1250000} to lowest terms by extracting and canceling out 16.

$$\frac{127251}{78125}\times 1.5\times 6.022\times 3.7320508075688776^{2}\left(0.7\times \frac{79^{2}}{197}+0.3\times \frac{49^{2}}{108}\right)$$

Convert decimal number 1.5 to fraction \frac{15}{10}. Reduce the fraction \frac{15}{10} to lowest terms by extracting and canceling out 5.

$$\frac{127251}{78125}\times \frac{3}{2}\times 6.022\times 3.7320508075688776^{2}\left(0.7\times \frac{79^{2}}{197}+0.3\times \frac{49^{2}}{108}\right)$$

Multiply \frac{127251}{78125} times \frac{3}{2} by multiplying numerator times numerator and denominator times denominator.

$$\frac{127251\times 3}{78125\times 2}\times 6.022\times 3.7320508075688776^{2}\left(0.7\times \frac{79^{2}}{197}+0.3\times \frac{49^{2}}{108}\right)$$

Do the multiplications in the fraction \frac{127251\times 3}{78125\times 2}.

$$\frac{381753}{156250}\times 6.022\times 3.7320508075688776^{2}\left(0.7\times \frac{79^{2}}{197}+0.3\times \frac{49^{2}}{108}\right)$$

Convert decimal number 6.022 to fraction \frac{6022}{1000}. Reduce the fraction \frac{6022}{1000} to lowest terms by extracting and canceling out 2.

$$\frac{381753}{156250}\times \frac{3011}{500}\times 3.7320508075688776^{2}\left(0.7\times \frac{79^{2}}{197}+0.3\times \frac{49^{2}}{108}\right)$$

Multiply \frac{381753}{156250} times \frac{3011}{500} by multiplying numerator times numerator and denominator times denominator.

$$\frac{381753\times 3011}{156250\times 500}\times 3.7320508075688776^{2}\left(0.7\times \frac{79^{2}}{197}+0.3\times \frac{49^{2}}{108}\right)$$

Do the multiplications in the fraction \frac{381753\times 3011}{156250\times 500}.

$$\frac{1149458283}{78125000}\times 3.7320508075688776^{2}\left(0.7\times \frac{79^{2}}{197}+0.3\times \frac{49^{2}}{108}\right)$$

Calculate 3.7320508075688776 to the power of 2 and get 13.92820323027551146165206812378176.

$$\frac{1149458283}{78125000}\times 13.92820323027551146165206812378176\left(0.7\times \frac{79^{2}}{197}+0.3\times \frac{49^{2}}{108}\right)$$

Convert decimal number 13.92820323027551146165206812378176 to fraction \frac{21762817547305486658831356443409}{10000000000}. Reduce the fraction \frac{21762817547305486658831356443409}{10000000000} to lowest terms by extracting and canceling out 1.

$$\frac{1149458283}{78125000}\times \frac{21762817547305486658831356443409}{1562500000000000000000000000000}\left(0.7\times \frac{79^{2}}{197}+0.3\times \frac{49^{2}}{108}\right)$$

Multiply \frac{1149458283}{78125000} times \frac{21762817547305486658831356443409}{1562500000000000000000000000000} by multiplying numerator times numerator and denominator times denominator.

$$\frac{1149458283\times 21762817547305486658831356443409}{78125000\times 1562500000000000000000000000000}\left(0.7\times \frac{79^{2}}{197}+0.3\times \frac{49^{2}}{108}\right)$$

Do the multiplications in the fraction \frac{1149458283\times 21762817547305486658831356443409}{78125000\times 1562500000000000000000000000000}.

$$\frac{25015450891168035971339697764001895806747}{122070312500000000000000000000000000000}\left(0.7\times \frac{79^{2}}{197}+0.3\times \frac{49^{2}}{108}\right)$$

Calculate 79 to the power of 2 and get 6241.

$$\frac{25015450891168035971339697764001895806747}{122070312500000000000000000000000000000}\left(0.7\times \frac{6241}{197}+0.3\times \frac{49^{2}}{108}\right)$$

Convert decimal number 0.7 to fraction \frac{7}{10}.

$$\frac{25015450891168035971339697764001895806747}{122070312500000000000000000000000000000}\left(\frac{7}{10}\times \frac{6241}{197}+0.3\times \frac{49^{2}}{108}\right)$$

Multiply \frac{7}{10} times \frac{6241}{197} by multiplying numerator times numerator and denominator times denominator.

$$\frac{25015450891168035971339697764001895806747}{122070312500000000000000000000000000000}\left(\frac{7\times 6241}{10\times 197}+0.3\times \frac{49^{2}}{108}\right)$$

Do the multiplications in the fraction \frac{7\times 6241}{10\times 197}.

$$\frac{25015450891168035971339697764001895806747}{122070312500000000000000000000000000000}\left(\frac{43687}{1970}+0.3\times \frac{49^{2}}{108}\right)$$

Calculate 49 to the power of 2 and get 2401.

$$\frac{25015450891168035971339697764001895806747}{122070312500000000000000000000000000000}\left(\frac{43687}{1970}+0.3\times \frac{2401}{108}\right)$$

Convert decimal number 0.3 to fraction \frac{3}{10}.

$$\frac{25015450891168035971339697764001895806747}{122070312500000000000000000000000000000}\left(\frac{43687}{1970}+\frac{3}{10}\times \frac{2401}{108}\right)$$

Multiply \frac{3}{10} times \frac{2401}{108} by multiplying numerator times numerator and denominator times denominator.

$$\frac{25015450891168035971339697764001895806747}{122070312500000000000000000000000000000}\left(\frac{43687}{1970}+\frac{3\times 2401}{10\times 108}\right)$$

Do the multiplications in the fraction \frac{3\times 2401}{10\times 108}.

$$\frac{25015450891168035971339697764001895806747}{122070312500000000000000000000000000000}\left(\frac{43687}{1970}+\frac{7203}{1080}\right)$$

Reduce the fraction \frac{7203}{1080} to lowest terms by extracting and canceling out 3.

$$\frac{25015450891168035971339697764001895806747}{122070312500000000000000000000000000000}\left(\frac{43687}{1970}+\frac{2401}{360}\right)$$

Least common multiple of 1970 and 360 is 70920. Convert \frac{43687}{1970} and \frac{2401}{360} to fractions with denominator 70920.

$$\frac{25015450891168035971339697764001895806747}{122070312500000000000000000000000000000}\left(\frac{1572732}{70920}+\frac{472997}{70920}\right)$$

Since \frac{1572732}{70920} and \frac{472997}{70920} have the same denominator, add them by adding their numerators.

$$\frac{25015450891168035971339697764001895806747}{122070312500000000000000000000000000000}\times \frac{1572732+472997}{70920}$$

Add 1572732 and 472997 to get 2045729.

$$\frac{25015450891168035971339697764001895806747}{122070312500000000000000000000000000000}\times \frac{2045729}{70920}$$

Multiply \frac{25015450891168035971339697764001895806747}{122070312500000000000000000000000000000} times \frac{2045729}{70920} by multiplying numerator times numerator and denominator times denominator.

$$\frac{25015450891168035971339697764001895806747\times 2045729}{122070312500000000000000000000000000000\times 70920}$$

Do the multiplications in the fraction \frac{25015450891168035971339697764001895806747\times 2045729}{122070312500000000000000000000000000000\times 70920}.

$$\frac{51174833336138295059612788567053834306840733563}{8657226562500000000000000000000000000000000}$$

Reduce the fraction \frac{51174833336138295059612788567053834306840733563}{8657226562500000000000000000000000000000000} to lowest terms by extracting and canceling out 9.

$$\frac{5686092592904255006623643174117092700760081507}{961914062500000000000000000000000000000000}$$

Factor

$$\frac{7 \cdot 17 \cdot 1571 \cdot 3011 \cdot 17191 \cdot 3 ^ {3} \cdot 23 ^ {2} \cdot 149011 ^ {2} \cdot 1361166949 ^ {2}}{197 \cdot 2 ^ {32} \cdot 5 ^ {43}} = 5911\frac{2.185694667553193 \times 10^{41}}{9.619140625 \times 10^{41}} = 5911.227223486251$$