Solve 100/6.05sqrt{{left(2.5/100right)}^2}+{left(0.005/6.05right)}^2

$$\frac{ 100 }{ 6.05 } \sqrt{ { \left( \frac{ 2.5 }{ 100 } \right) }^{ 2 } } + { \left( \frac{ 0.005 }{ 6.05 } \right) }^{ 2 }$$

Evaluate

$$\frac{605001}{1464100}\approx 0.413223824$$

Solution Steps

Expand \frac{100}{6.05} by multiplying both numerator and the denominator by 100.

$$\frac{10000}{605}\sqrt{\left(\frac{2.5}{100}\right)^{2}}+\left(\frac{0.005}{6.05}\right)^{2}$$

Reduce the fraction \frac{10000}{605} to lowest terms by extracting and canceling out 5.

$$\frac{2000}{121}\sqrt{\left(\frac{2.5}{100}\right)^{2}}+\left(\frac{0.005}{6.05}\right)^{2}$$

Expand \frac{2.5}{100} by multiplying both numerator and the denominator by 10.

$$\frac{2000}{121}\sqrt{\left(\frac{25}{1000}\right)^{2}}+\left(\frac{0.005}{6.05}\right)^{2}$$

Reduce the fraction \frac{25}{1000} to lowest terms by extracting and canceling out 25.

$$\frac{2000}{121}\sqrt{\left(\frac{1}{40}\right)^{2}}+\left(\frac{0.005}{6.05}\right)^{2}$$

Calculate \frac{1}{40} to the power of 2 and get \frac{1}{1600}.

$$\frac{2000}{121}\sqrt{\frac{1}{1600}}+\left(\frac{0.005}{6.05}\right)^{2}$$

Rewrite the square root of the division \frac{1}{1600} as the division of square roots \frac{\sqrt{1}}{\sqrt{1600}}. Take the square root of both numerator and denominator.

$$\frac{2000}{121}\times \frac{1}{40}+\left(\frac{0.005}{6.05}\right)^{2}$$

Multiply \frac{2000}{121} and \frac{1}{40} to get \frac{50}{121}.

$$\frac{50}{121}+\left(\frac{0.005}{6.05}\right)^{2}$$

Expand \frac{0.005}{6.05} by multiplying both numerator and the denominator by 1000.

$$\frac{50}{121}+\left(\frac{5}{6050}\right)^{2}$$

Reduce the fraction \frac{5}{6050} to lowest terms by extracting and canceling out 5.

$$\frac{50}{121}+\left(\frac{1}{1210}\right)^{2}$$

Calculate \frac{1}{1210} to the power of 2 and get \frac{1}{1464100}.

$$\frac{50}{121}+\frac{1}{1464100}$$

Add \frac{50}{121} and \frac{1}{1464100} to get \frac{605001}{1464100}.

$$\frac{605001}{1464100}$$

Factor

$$\frac{3 \cdot 201667}{2 ^ {2} \cdot 5 ^ {2} \cdot 11 ^ {4}} = 0.41322382350932313$$