Proof of inequality using Cauchy–Schwarz inequality

Question

How I can prove this inequality? How can I prove it using Cauchy–Schwarz inequality?

Let $a_1,...,a_n,b_1,....,b_n$ are any real numbers.

$\sqrt {\sum_{k=1}^n (a_k+b_k)^2)} \leq \sqrt {\sum_{k=1}^n {a_k}^2} \sqrt {\sum_{k=1}^n {b_k}^2}$

Answer 1

This is false when $a_1 = b_1= 1$ and $a_k = b_k = 0$ for $k \ne 1$.