Conceptual Doubt in Algebra

[daxita01]

In the above question, if I take a square root of the first equation (i.e squaring both the sides), will a+b^2 (the LHS) be actually equal to the ABSOLUTE value of a+b? Making the RHS +/- 7?

Also if we open the algebraic property, (a+b)^2, we get a^2 + b^2 = 25, can we not take a square root of this and get a+b = 5?

[cylverixxx]

@daxita01

In the above question, if I take a square root of the first equation (i.e squaring both the sides), will a+b^2 (the LHS) be actually equal to the ABSOLUTE value of a+b? Making the RHS +/- 7?

Do you mean (a + b)^2 = 49 \implies |a + b| = 7. If so, then yes that is right.

@daxita01

Also if we open the algebraic property, (a+b)^2, we get a^2 + b^2 = 25, can we not take a square root of this and get a+b = 5?

But \sqrt{a^2 + b^2} \neq a + b though.

[daxita01]

yes, that’s what I meant!
Alright I do understand now that we can’t take a square root of (a+b)^2 to arrive at 5.
Thank you so much