Solve sqrt{{left(1/450right)}^2}+1/6

$$\sqrt{ { \left( \frac{ 1 }{ 450 } \right) }^{ 2 } } + \frac{ 1 }{ 6 }$$

Evaluate

$$\frac{38}{225}\approx 0.168888889$$

Solution Steps

Calculate \frac{1}{450} to the power of 2 and get \frac{1}{202500}.

$$\sqrt{\frac{1}{202500}}+\frac{1}{6}$$

Rewrite the square root of the division \frac{1}{202500} as the division of square roots \frac{\sqrt{1}}{\sqrt{202500}}. Take the square root of both numerator and denominator.

$$\frac{1}{450}+\frac{1}{6}$$

Least common multiple of 450 and 6 is 450. Convert \frac{1}{450} and \frac{1}{6} to fractions with denominator 450.

$$\frac{1}{450}+\frac{75}{450}$$

Since \frac{1}{450} and \frac{75}{450} have the same denominator, add them by adding their numerators.

$$\frac{1+75}{450}$$

Add 1 and 75 to get 76.

$$\frac{76}{450}$$

Reduce the fraction \frac{76}{450} to lowest terms by extracting and canceling out 2.

$$\frac{38}{225}$$

Factor

$$\frac{2 \cdot 19}{3 ^ {2} \cdot 5 ^ {2}} = 0.1688888888888889$$