\(\sqrt{(a+b)}=\sqrt{a}+\sqrt{b} \) Prove if these equations are true, show your working out
2. \(\sqrt{(a-b)}=\sqrt{a}-\sqrt{b}\)
+128408 √ [ a + b ] = √a + √b square both sides
[√ [ a + b ] ]^2 = [ √a + √b ]^2
a + b = [ √a + √b ] [ √a + √b ]
a + b = [√a ]^2 + 2 √a√b + [√b ]^2
a + b = a + 2 √a√b + b
If we subtract a, b from both sides, we have that
0 = 2 √a√b
This is not true unless a or b [or both ] = 0 ....so.....the original equation, in general, isn't true, either
Using similar procedures, the second one will be
a - b = a - 2 √a√b + b subtract a, b from both sides
-2b = - 2√a√b divide both sides by -2
b = √a√b and this is only true if a = b and a,b ≥ 0
So....the second one isn't true, in general, either
