Round your lips into a tight circle. Lift the back of your tongue toward the soft palate and add voice.

Americans pronounce whales as WAYLZ (/weɪlz/). The L in "whales" is a dark L — the back of the tongue rises toward the soft palate, adding a small "uh" quality before the L. This is called the Dark L vs Light L, and it's one of the defining features of casual American English. It comes out as WAYLZ. You'll hear it in sentences like "Whales migrate thousands of miles every year to breed".
Record yourself saying "whales" and play it back. The mic stays on your device — nothing's uploaded.
1 syllable, 4 sounds. Explore each sound's mouth shape and how it's made.
Round your lips into a tight circle. Lift the back of your tongue toward the soft palate and add voice.

Start with your jaw slightly open and the front of your tongue forward and slightly up. Glide upward, your jaw closes a little more and your tongue arches higher toward the roof of the mouth.
Keep the tongue tip down and pull the back of the tongue up toward the throat. The 'dark' sound comes from the back.

Same position as S, but add vocal cord vibration. Feel the buzz.

The textbook way isn't wrong — it's just not how anyone actually says it.
The L in "whales" is a dark L — the back of the tongue rises toward the soft palate, adding a small "uh" quality before the L. Dark L adds a small schwa-like "uh" before the L. The back of the tongue lifts toward the soft palate.