Solve {l}{2*(0.009)^{2}+(0.019)^{2}*2}{+(0.001)^{2}+(0.021)^{2}+(0.031)^2}{+(0.049)^2+(0.041)^2+(0.011)^2}

$$\left. \begin{array} { l } { 2 \times ( 0.009 ) ^ { 2 } + ( 0.019 ) ^ { 2 } \times 2 } \\ { + ( 0.001 ) ^ { 2 } + ( 0.021 ) ^ { 2 } + ( 0.031 ) ^ { 2 } } \\ { + ( 0.049 ) ^ { 2 } + ( 0.041 ) ^ { 2 } + ( 0.011 ) ^ { 2 } } \end{array} \right.$$

Evaluate

$$0.00649$$

Solution Steps

Calculate 0.009 to the power of 2 and get 0.000081.

$$2\times 0.000081+0.019^{2}\times 2+0.001^{2}+0.021^{2}+0.031^{2}+0.049^{2}+0.041^{2}+0.011^{2}$$

Multiply 2 and 0.000081 to get 0.000162.

$$0.000162+0.019^{2}\times 2+0.001^{2}+0.021^{2}+0.031^{2}+0.049^{2}+0.041^{2}+0.011^{2}$$

Calculate 0.019 to the power of 2 and get 0.000361.

$$0.000162+0.000361\times 2+0.001^{2}+0.021^{2}+0.031^{2}+0.049^{2}+0.041^{2}+0.011^{2}$$

Multiply 0.000361 and 2 to get 0.000722.

$$0.000162+0.000722+0.001^{2}+0.021^{2}+0.031^{2}+0.049^{2}+0.041^{2}+0.011^{2}$$

Add 0.000162 and 0.000722 to get 0.000884.

$$0.000884+0.001^{2}+0.021^{2}+0.031^{2}+0.049^{2}+0.041^{2}+0.011^{2}$$

Calculate 0.001 to the power of 2 and get 0.000001.

$$0.000884+0.000001+0.021^{2}+0.031^{2}+0.049^{2}+0.041^{2}+0.011^{2}$$

Add 0.000884 and 0.000001 to get 0.000885.

$$0.000885+0.021^{2}+0.031^{2}+0.049^{2}+0.041^{2}+0.011^{2}$$

Calculate 0.021 to the power of 2 and get 0.000441.

$$0.000885+0.000441+0.031^{2}+0.049^{2}+0.041^{2}+0.011^{2}$$

Add 0.000885 and 0.000441 to get 0.001326.

$$0.001326+0.031^{2}+0.049^{2}+0.041^{2}+0.011^{2}$$

Calculate 0.031 to the power of 2 and get 0.000961.

$$0.001326+0.000961+0.049^{2}+0.041^{2}+0.011^{2}$$

Add 0.001326 and 0.000961 to get 0.002287.

$$0.002287+0.049^{2}+0.041^{2}+0.011^{2}$$

Calculate 0.049 to the power of 2 and get 0.002401.

$$0.002287+0.002401+0.041^{2}+0.011^{2}$$

Add 0.002287 and 0.002401 to get 0.004688.

$$0.004688+0.041^{2}+0.011^{2}$$

Calculate 0.041 to the power of 2 and get 0.001681.

$$0.004688+0.001681+0.011^{2}$$

Add 0.004688 and 0.001681 to get 0.006369.

$$0.006369+0.011^{2}$$

Calculate 0.011 to the power of 2 and get 0.000121.

$$0.006369+0.000121$$

Add 0.006369 and 0.000121 to get 0.00649.

$$0.00649$$

Factor

$$\frac{11 \cdot 59}{2 ^ {5} \cdot 5 ^ {5}} = 0.00649$$