Evaluate

Problem

√(,1/3*(0.0001)2+1/3*(−0.0005)2+1/3*(0.0006)2+1/3*(−0.0001)2)

Solution

1. Factor out the common term 1/3 from each term inside the square root.

√(,1/3*((0.0001)2+(−0.0005)2+(0.0006)2+(−0.0001)2))

2. Square each of the decimal values inside the parentheses.

(0.0001)2=0.00000001

(−0.0005)2=0.00000025

(0.0006)2=0.00000036

(−0.0001)2=0.00000001

3. Sum the squared values together.

0.00000001+0.00000025+0.00000036+0.00000001=0.00000063

4. Multiply the sum by the factor 1/3

1/3×0.00000063=0.00000021

5. Evaluate the square root of the resulting value.

√(,0.00000021)≈0.000458257569

Final Answer

√(,1/3*(0.0001)2+1/3*(−0.0005)2+1/3*(0.0006)2+1/3*(−0.0001)2)=√(,0.00000021)≈0.000458257569

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