If p and q are positive real numbers such that `p^2+""q^2=""1` , then the maximum value of `(p""+""q)` is (1) 2 (2) 1/2 (3) `1/(sqrt(2))` (4) `sqrt(2)`

Explanation

To find the maximum value of \( p + q \) given that \( p^2 + q^2 = 1 \), we can follow these steps:

### Step 1: Express \( q \) in terms of \( p \)
From the equation \( p^2 + q^2 = 1 \), we can express \( q \) as:
\[ q = \sqrt{1 - p^2} \]

...