Which of the following operations could make the expression x2+8x√3 a perfect square?
Add(4√3)2
Subtract8x√3
For making this expression a perfect square,
x2+8x√3
=x2+2×4√3×x (here the (4√3)2 term is missing which is required to make the expression a perfect square)
So, We should add (4√3)2
⇒x2+2×4√3×x+(4√3)2
⇒(x+4√3)2
So if the term (4√3)2 is added, the expression x2+8x√3 becomes a perfect square.
Alternatively we can make the expression x2+8x√3 equal \(x^2\) (a perfect square) by subtracting the expression 8x√3.