Solve sqrt{(-1/30)^2}+(-1/12)^2+(-1/16)^2=

$$\sqrt { ( - \frac { 1 } { 30 } ) ^ { 2 } } + ( - \frac { 1 } { 12 } ) ^ { 2 } + ( \frac { - 1 } { 16 } ) ^ { 2 } =$$

Evaluate

$$\frac{509}{11520}\approx 0.044184028$$

Solution Steps

Calculate -\frac{1}{30} to the power of 2 and get \frac{1}{900}.

$$\sqrt{\frac{1}{900}}+\left(-\frac{1}{12}\right)^{2}+\left(\frac{-1}{16}\right)^{2}$$

Rewrite the square root of the division \frac{1}{900} as the division of square roots \frac{\sqrt{1}}{\sqrt{900}}. Take the square root of both numerator and denominator.

$$\frac{1}{30}+\left(-\frac{1}{12}\right)^{2}+\left(\frac{-1}{16}\right)^{2}$$

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

$$\frac{1}{30}+\frac{1}{144}+\left(\frac{-1}{16}\right)^{2}$$

Add \frac{1}{30} and \frac{1}{144} to get \frac{29}{720}.

$$\frac{29}{720}+\left(\frac{-1}{16}\right)^{2}$$

Fraction \frac{-1}{16} can be rewritten as -\frac{1}{16} by extracting the negative sign.

$$\frac{29}{720}+\left(-\frac{1}{16}\right)^{2}$$

Calculate -\frac{1}{16} to the power of 2 and get \frac{1}{256}.

$$\frac{29}{720}+\frac{1}{256}$$

Add \frac{29}{720} and \frac{1}{256} to get \frac{509}{11520}.

$$\frac{509}{11520}$$

Factor

$$\frac{509}{2 ^ {8} \cdot 3 ^ {2} \cdot 5} = 0.04418402777777778$$