Question

It is given that A = B2. If A = 100+ 0.20, then B
is equal to
(1) 10.1 0.20 (2) 100.02
831 10 0.01 (4) 10 ± 0.1​

Answer 1

answer : 10 ± 0.01

explanation : it is given that A = B²

and A = (100 ± 0.2)

here 100 is value of A and 0.2 is error in this value.

first of all, we have to find value of B

A = 100, B = ?

expression is A = B²

or, 100 = B²

or, (10)² = B² => B = 10

now To error in value of B :

expression ⇒ A = B²

taking log both sides,

logA = logB²

or, logA = 2logB

now differentiating both sides,

dA/A = 2dB/B

or, ∆A/A = 2∆B/B , here ∆A and ∆B denotes error in A and B respectively.

here , ∆A = 0.2, A = 100, B = 10

so, 0.2/100 = 2 × ∆B/10

or, 0.01 = ∆B

hence, appropriate value of B can be written as (10 ± 0.01)