Adding Two Directions

A vector database stores every document embedding L2-normalized — each stored vector is scaled to length $1$ before it is written to disk, so only its direction survives.

Two documents arrive with these raw embeddings:

The database normalizes each one on the way in, producing stored vectors $\hat{d_1}$ and $\hat{d_2}$. A clustering job then forms a topic vector by summing the two stored vectors:

$t = \hat{d_1} + \hat{d_2}$

What is $\lVert t \rVert$?

Round your answer to two decimal places.