Solve 0.97*(frac{sqrt{36}*9.37}{4.231+3.093})+11.4^2=

$$0.97 \times ( \frac { \sqrt { 36 } \times 9.37 } { 4.231 + 3.093 } ) + 11.4 ^ { 2 } =$$

Evaluate

$$\frac{25159011}{183100}\approx 137.405849263$$

Solution Steps

Calculate the square root of 36 and get 6.

$$0.97\times \frac{9.37\times 6}{4.231+3.093}+11.4^{2}$$

Multiply 9.37 and 6 to get 56.22.

$$0.97\times \frac{56.22}{4.231+3.093}+11.4^{2}$$

Add 4.231 and 3.093 to get 7.324.

$$0.97\times \frac{56.22}{7.324}+11.4^{2}$$

Expand \frac{56.22}{7.324} by multiplying both numerator and the denominator by 1000.

$$0.97\times \frac{56220}{7324}+11.4^{2}$$

Reduce the fraction \frac{56220}{7324} to lowest terms by extracting and canceling out 4.

$$0.97\times \frac{14055}{1831}+11.4^{2}$$

Convert decimal number 0.97 to fraction \frac{97}{100}.

$$\frac{97}{100}\times \frac{14055}{1831}+11.4^{2}$$

Multiply \frac{97}{100} times \frac{14055}{1831} by multiplying numerator times numerator and denominator times denominator.

$$\frac{97\times 14055}{100\times 1831}+11.4^{2}$$

Do the multiplications in the fraction \frac{97\times 14055}{100\times 1831}.

$$\frac{1363335}{183100}+11.4^{2}$$

Reduce the fraction \frac{1363335}{183100} to lowest terms by extracting and canceling out 5.

$$\frac{272667}{36620}+11.4^{2}$$

Calculate 11.4 to the power of 2 and get 129.96.

$$\frac{272667}{36620}+129.96$$

Convert decimal number 129.96 to fraction \frac{12996}{100}. Reduce the fraction \frac{12996}{100} to lowest terms by extracting and canceling out 4.

$$\frac{272667}{36620}+\frac{3249}{25}$$

Least common multiple of 36620 and 25 is 183100. Convert \frac{272667}{36620} and \frac{3249}{25} to fractions with denominator 183100.

$$\frac{1363335}{183100}+\frac{23795676}{183100}$$

Since \frac{1363335}{183100} and \frac{23795676}{183100} have the same denominator, add them by adding their numerators.

$$\frac{1363335+23795676}{183100}$$

Add 1363335 and 23795676 to get 25159011.

$$\frac{25159011}{183100}$$

Factor

$$\frac{3 \cdot 31 \cdot 270527}{1831 \cdot 2 ^ {2} \cdot 5 ^ {2}} = 137\frac{74311}{183100} = 137.40584926269798$$