Answer:
Square the expressions to see the difference.
Step-by-step explanation:
[tex]$ \sqrt{(m + n)} $[/tex].
Squaring this we have: [tex]$ (\sqrt{m + n})^2 = m + n $[/tex]
Now, [tex]$ \sqrt{m} + \sqrt{n} $[/tex]
Squaring this we get: [tex]$ (\sqrt{m})^2 + (\sqrt{n})^2 = m + n + 2 \sqrt{mn} $[/tex]
For the two expressions to be equal, we should have
[tex]$ m + n = m + n +2\sqrt{mn} $[/tex] ⇔ [tex]$ \sqrt{mn} = 0 $[/tex].
This is possible iff mn = 0. i.e, m = 0 or n = 0.
Otherwise, they are not equal.
When m = 5 and n = 4.
[tex]$ \sqrt{5 + 4} = \sqrt{9} = 3 $[/tex]
[tex]$ \sqrt{5} + \sqrt{4} = \sqrt{5} + 2 $[/tex]
First is an integer. Second is an irrational number.
Clearly, they are not equal.
