Solve (2*15.2*0.03/(15.20^{2-13^{2})})^{2}+(2*13*0.03/(15.20^2-13^2))^2+(0.03/82.16)^2

$$( \frac { 2 \times 15.2 \times 0.03 } { ( 15.20 ^ { 2 } - 13 ^ { 2 } ) } ) ^ { 2 } + ( \frac { 2 \times 13 \times 0.03 } { ( 15.20 ^ { 2 } - 13 ^ { 2 } ) } ) ^ { 2 } + ( \frac { 0.03 } { 82.16 } ) ^ { 2 }$$

Evaluate

$$\frac{168833655689}{451067935489600}\approx 0.000374298$$

Solution Steps

Multiply 2 and 15.2 to get 30.4.

$$\left(\frac{30.4\times 0.03}{15.2^{2}-13^{2}}\right)^{2}+\left(\frac{2\times 13\times 0.03}{15.2^{2}-13^{2}}\right)^{2}+\left(\frac{0.03}{82.16}\right)^{2}$$

Multiply 30.4 and 0.03 to get 0.912.

$$\left(\frac{0.912}{15.2^{2}-13^{2}}\right)^{2}+\left(\frac{2\times 13\times 0.03}{15.2^{2}-13^{2}}\right)^{2}+\left(\frac{0.03}{82.16}\right)^{2}$$

Calculate 15.2 to the power of 2 and get 231.04.

$$\left(\frac{0.912}{231.04-13^{2}}\right)^{2}+\left(\frac{2\times 13\times 0.03}{15.2^{2}-13^{2}}\right)^{2}+\left(\frac{0.03}{82.16}\right)^{2}$$

Calculate 13 to the power of 2 and get 169.

$$\left(\frac{0.912}{231.04-169}\right)^{2}+\left(\frac{2\times 13\times 0.03}{15.2^{2}-13^{2}}\right)^{2}+\left(\frac{0.03}{82.16}\right)^{2}$$

Subtract 169 from 231.04 to get 62.04.

$$\left(\frac{0.912}{62.04}\right)^{2}+\left(\frac{2\times 13\times 0.03}{15.2^{2}-13^{2}}\right)^{2}+\left(\frac{0.03}{82.16}\right)^{2}$$

Expand \frac{0.912}{62.04} by multiplying both numerator and the denominator by 1000.

$$\left(\frac{912}{62040}\right)^{2}+\left(\frac{2\times 13\times 0.03}{15.2^{2}-13^{2}}\right)^{2}+\left(\frac{0.03}{82.16}\right)^{2}$$

Reduce the fraction \frac{912}{62040} to lowest terms by extracting and canceling out 24.

$$\left(\frac{38}{2585}\right)^{2}+\left(\frac{2\times 13\times 0.03}{15.2^{2}-13^{2}}\right)^{2}+\left(\frac{0.03}{82.16}\right)^{2}$$

Calculate \frac{38}{2585} to the power of 2 and get \frac{1444}{6682225}.

$$\frac{1444}{6682225}+\left(\frac{2\times 13\times 0.03}{15.2^{2}-13^{2}}\right)^{2}+\left(\frac{0.03}{82.16}\right)^{2}$$

Multiply 2 and 13 to get 26.

$$\frac{1444}{6682225}+\left(\frac{26\times 0.03}{15.2^{2}-13^{2}}\right)^{2}+\left(\frac{0.03}{82.16}\right)^{2}$$

Multiply 26 and 0.03 to get 0.78.

$$\frac{1444}{6682225}+\left(\frac{0.78}{15.2^{2}-13^{2}}\right)^{2}+\left(\frac{0.03}{82.16}\right)^{2}$$

Calculate 15.2 to the power of 2 and get 231.04.

$$\frac{1444}{6682225}+\left(\frac{0.78}{231.04-13^{2}}\right)^{2}+\left(\frac{0.03}{82.16}\right)^{2}$$

Calculate 13 to the power of 2 and get 169.

$$\frac{1444}{6682225}+\left(\frac{0.78}{231.04-169}\right)^{2}+\left(\frac{0.03}{82.16}\right)^{2}$$

Subtract 169 from 231.04 to get 62.04.

$$\frac{1444}{6682225}+\left(\frac{0.78}{62.04}\right)^{2}+\left(\frac{0.03}{82.16}\right)^{2}$$

Expand \frac{0.78}{62.04} by multiplying both numerator and the denominator by 100.

$$\frac{1444}{6682225}+\left(\frac{78}{6204}\right)^{2}+\left(\frac{0.03}{82.16}\right)^{2}$$

Reduce the fraction \frac{78}{6204} to lowest terms by extracting and canceling out 6.

$$\frac{1444}{6682225}+\left(\frac{13}{1034}\right)^{2}+\left(\frac{0.03}{82.16}\right)^{2}$$

Calculate \frac{13}{1034} to the power of 2 and get \frac{169}{1069156}.

$$\frac{1444}{6682225}+\frac{169}{1069156}+\left(\frac{0.03}{82.16}\right)^{2}$$

Add \frac{1444}{6682225} and \frac{169}{1069156} to get \frac{10001}{26728900}.

$$\frac{10001}{26728900}+\left(\frac{0.03}{82.16}\right)^{2}$$

Expand \frac{0.03}{82.16} by multiplying both numerator and the denominator by 100.

$$\frac{10001}{26728900}+\left(\frac{3}{8216}\right)^{2}$$

Calculate \frac{3}{8216} to the power of 2 and get \frac{9}{67502656}.

$$\frac{10001}{26728900}+\frac{9}{67502656}$$

Add \frac{10001}{26728900} and \frac{9}{67502656} to get \frac{168833655689}{451067935489600}.

$$\frac{168833655689}{451067935489600}$$

Factor

$$\frac{109 \cdot 1548932621}{2 ^ {6} \cdot 5 ^ {2} \cdot 11 ^ {2} \cdot 13 ^ {2} \cdot 47 ^ {2} \cdot 79 ^ {2}} = 0.0003742976221658139$$