Solve sqrt{{left(0.02/5.22right)}^2+{left(0.02/10.26right)}^2+{left(0.005/750right)}^2}

$$\sqrt{ { \left( \frac{ 0.02 }{ 5.22 } \right) }^{ 2 } + { \left( \frac{ 0.02 }{ 10.26 } \right) }^{ 2 } + { \left( \frac{ 0.005 }{ 750 } \right) }^{ 2 } }$$

Evaluate

$$\frac{\sqrt{10225024591681}}{743850000}\approx 0.004298796$$

Solution Steps

Expand \frac{0.02}{5.22} by multiplying both numerator and the denominator by 100.

$$\sqrt{\left(\frac{2}{522}\right)^{2}+\left(\frac{0.02}{10.26}\right)^{2}+\left(\frac{0.005}{750}\right)^{2}}$$

Reduce the fraction \frac{2}{522} to lowest terms by extracting and canceling out 2.

$$\sqrt{\left(\frac{1}{261}\right)^{2}+\left(\frac{0.02}{10.26}\right)^{2}+\left(\frac{0.005}{750}\right)^{2}}$$

Calculate \frac{1}{261} to the power of 2 and get \frac{1}{68121}.

$$\sqrt{\frac{1}{68121}+\left(\frac{0.02}{10.26}\right)^{2}+\left(\frac{0.005}{750}\right)^{2}}$$

Expand \frac{0.02}{10.26} by multiplying both numerator and the denominator by 100.

$$\sqrt{\frac{1}{68121}+\left(\frac{2}{1026}\right)^{2}+\left(\frac{0.005}{750}\right)^{2}}$$

Reduce the fraction \frac{2}{1026} to lowest terms by extracting and canceling out 2.

$$\sqrt{\frac{1}{68121}+\left(\frac{1}{513}\right)^{2}+\left(\frac{0.005}{750}\right)^{2}}$$

Calculate \frac{1}{513} to the power of 2 and get \frac{1}{263169}.

$$\sqrt{\frac{1}{68121}+\frac{1}{263169}+\left(\frac{0.005}{750}\right)^{2}}$$

Add \frac{1}{68121} and \frac{1}{263169} to get \frac{4090}{221325129}.

$$\sqrt{\frac{4090}{221325129}+\left(\frac{0.005}{750}\right)^{2}}$$

Expand \frac{0.005}{750} by multiplying both numerator and the denominator by 1000.

$$\sqrt{\frac{4090}{221325129}+\left(\frac{5}{750000}\right)^{2}}$$

Reduce the fraction \frac{5}{750000} to lowest terms by extracting and canceling out 5.

$$\sqrt{\frac{4090}{221325129}+\left(\frac{1}{150000}\right)^{2}}$$

Calculate \frac{1}{150000} to the power of 2 and get \frac{1}{22500000000}.

$$\sqrt{\frac{4090}{221325129}+\frac{1}{22500000000}}$$

Add \frac{4090}{221325129} and \frac{1}{22500000000} to get \frac{10225024591681}{553312822500000000}.

$$\sqrt{\frac{10225024591681}{553312822500000000}}$$

Rewrite the square root of the division \sqrt{\frac{10225024591681}{553312822500000000}} as the division of square roots \frac{\sqrt{10225024591681}}{\sqrt{553312822500000000}}.

$$\frac{\sqrt{10225024591681}}{\sqrt{553312822500000000}}$$

Calculate the square root of 553312822500000000 and get 743850000.

$$\frac{\sqrt{10225024591681}}{743850000}$$