Question

To simplify (3+√3)(3-√3) which property we can use (√a+√b)(√a-√b)= a-b (a+√b)(a-√b)= a²-b (a+b)(a-b)= a²-b² Either (b) or (c)​

Answer 1

Answer:

Why is √a+√b ≠ √(a+b)?

Let’s take a look at the equation.

(For simplicity’s sake, let’s assume that we are talking about real numbers, and not complex numbers, i.e. the square root of negative numbers is not defined. So a and b are positive.)

√a+√b=√((√a+√b)²)=√((√a+√b)·(√a+√b))=√(√a·(√a+√b)+√b·(√a+√b))

=√(√a·√a+√a·√b+√b·√a+√b·√b)=√(a+2·√a·√b+b)≠√(a+b)

Note: The last inequation is only true if both a and b are not equal to 0.