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

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

Evaluate

$$\frac{\sqrt{48298}}{4959}\approx 0.044317011$$

Solution Steps

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

$$\sqrt{\left(\frac{2}{522}\right)^{2}+\left(\frac{0.02}{10.26}\right)^{1}}$$

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

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

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

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

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

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

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

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

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

$$\sqrt{\frac{1}{68121}+\frac{1}{513}}$$

Add \frac{1}{68121} and \frac{1}{513} to get \frac{2542}{1294299}.

$$\sqrt{\frac{2542}{1294299}}$$

Rewrite the square root of the division \sqrt{\frac{2542}{1294299}} as the division of square roots \frac{\sqrt{2542}}{\sqrt{1294299}}.

$$\frac{\sqrt{2542}}{\sqrt{1294299}}$$

Factor 1294299=261^{2}\times 19. Rewrite the square root of the product \sqrt{261^{2}\times 19} as the product of square roots \sqrt{261^{2}}\sqrt{19}. Take the square root of 261^{2}.

$$\frac{\sqrt{2542}}{261\sqrt{19}}$$

Rationalize the denominator of \frac{\sqrt{2542}}{261\sqrt{19}} by multiplying numerator and denominator by \sqrt{19}.

$$\frac{\sqrt{2542}\sqrt{19}}{261\left(\sqrt{19}\right)^{2}}$$

The square of \sqrt{19} is 19.

$$\frac{\sqrt{2542}\sqrt{19}}{261\times 19}$$

To multiply \sqrt{2542} and \sqrt{19}, multiply the numbers under the square root.

$$\frac{\sqrt{48298}}{261\times 19}$$

Multiply 261 and 19 to get 4959.

$$\frac{\sqrt{48298}}{4959}$$