The "d" is not silent. Think of the word "bread" and add a 'soft' "th" at the end of it.
New words, one handy idiom, and a 2-minute quiz — delivered to your inbox to keep your streak alive.
Breadth is pronounced with the "d" but it's more like half of the "d" sound, not even quite that. Instead of pronouncing the entire "d" sound, you only pronounce the beginning tip of it. It's just like saying bread, only as soon as you begin the "d" sound you move into the "th" sound. Basically you just touch your front teeth together right before pronouncing the "th" sound.
Using a Critical Pronouncing of the English Language, by John Walker, from 1849, page 59, we have the following: "dth" disaperars, in spite of authorities to pronounce the "d".