Solve sqrt{(0.25/3)^2+(0.05/3)^2+(0.05/2)^2}

$$\sqrt { ( \frac { 0.25 } { 3 } ) ^ { 2 } + ( \frac { 0.05 } { 3 } ) ^ { 2 } + ( 0.05 / 2 ) ^ { 2 } }$$

Evaluate

$$\frac{\sqrt{113}}{120}\approx 0.088584548$$

Solution Steps

Expand \frac{0.25}{3} by multiplying both numerator and the denominator by 100.

$$\sqrt{\left(\frac{25}{300}\right)^{2}+\left(\frac{0.05}{3}\right)^{2}+\left(\frac{0.05}{2}\right)^{2}}$$

Reduce the fraction \frac{25}{300} to lowest terms by extracting and canceling out 25.

$$\sqrt{\left(\frac{1}{12}\right)^{2}+\left(\frac{0.05}{3}\right)^{2}+\left(\frac{0.05}{2}\right)^{2}}$$

Calculate \frac{1}{12} to the power of 2 and get \frac{1}{144}.

$$\sqrt{\frac{1}{144}+\left(\frac{0.05}{3}\right)^{2}+\left(\frac{0.05}{2}\right)^{2}}$$

Expand \frac{0.05}{3} by multiplying both numerator and the denominator by 100.

$$\sqrt{\frac{1}{144}+\left(\frac{5}{300}\right)^{2}+\left(\frac{0.05}{2}\right)^{2}}$$

Reduce the fraction \frac{5}{300} to lowest terms by extracting and canceling out 5.

$$\sqrt{\frac{1}{144}+\left(\frac{1}{60}\right)^{2}+\left(\frac{0.05}{2}\right)^{2}}$$

Calculate \frac{1}{60} to the power of 2 and get \frac{1}{3600}.

$$\sqrt{\frac{1}{144}+\frac{1}{3600}+\left(\frac{0.05}{2}\right)^{2}}$$

Add \frac{1}{144} and \frac{1}{3600} to get \frac{13}{1800}.

$$\sqrt{\frac{13}{1800}+\left(\frac{0.05}{2}\right)^{2}}$$

Expand \frac{0.05}{2} by multiplying both numerator and the denominator by 100.

$$\sqrt{\frac{13}{1800}+\left(\frac{5}{200}\right)^{2}}$$

Reduce the fraction \frac{5}{200} to lowest terms by extracting and canceling out 5.

$$\sqrt{\frac{13}{1800}+\left(\frac{1}{40}\right)^{2}}$$

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

$$\sqrt{\frac{13}{1800}+\frac{1}{1600}}$$

Add \frac{13}{1800} and \frac{1}{1600} to get \frac{113}{14400}.

$$\sqrt{\frac{113}{14400}}$$

Rewrite the square root of the division \sqrt{\frac{113}{14400}} as the division of square roots \frac{\sqrt{113}}{\sqrt{14400}}.

$$\frac{\sqrt{113}}{\sqrt{14400}}$$

Calculate the square root of 14400 and get 120.

$$\frac{\sqrt{113}}{120}$$