For what value of A, will the expression (13.56 × 13.56 + 13.56 × A + 0.04 × 0.04) be a perfect square?

Correct option is D

Given:

Expression: 13.56 × 13.56 + 13.56 × A + 0.04 × 0.04

Formula Used:

​$$(a + b)^2 = a^2 + 2ab + b^2$$​​

Solution:

Let the expression be $$(13.56 + 0.04)^2$$​​
So, 

​$$(13.56 + 0.04)^2 = 13.56^2 + 2 \times 13.56 \times 0.04 + 0.04^2$$​​

​$$=13.56^2 + 13.56 \times 0.08 + 0.04^2$$​​

Comparing with given expression:

A must be 0.08