Can we write $sqrt(9+4)$ as $sqrt9 + sqrt4$ ? Justify?

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Answer 1 · 2017-08-05T19:19:26

No.

$s = sqrt(9+4)$ if and only if $s^2 = 9+4 = 13$

$sqrt9+sqrt4 = 3+2 = 5$ and $5^2 != 13$

So $5 != sqrt(9+4)$

Can we write sqrt(9+4)sqrt(9+4) as sqrt9 + sqrt4sqrt9 + sqrt4? Justify?