To determine the correct value for √AB, we start with the given measurements: A=1.0m±0.2m B=2.0m±0.2m First, calculate Y=√AB : Y=√(1.0)(2.0)=√2.0≈1.414m Rounding this to two significant digits: Y=1.4m Next, calculate the uncertainty in Y : The relative uncertainty in Y is given by:
∆Y
Y
=
1
2
(
∆A
A
+
∆B
B
) Substitute the values:
∆Y
Y
=
1
2
(
0.2
1.0
+
0.2
2.0
)=
1
2
(0.2+0.1)=
0.3
2
Calculate ∆Y : ∆Y=
0.3×1.4
2
=0.21 Rounding off to one significant digit, ∆Y≈0.2m. Thus, the correct value for √AB is: 1.4m±0.2m