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Yes. When there is more than one radical, you first need to identify the primary radical. The convention is for the primary radical to be determined by its placement: (1) top, (2) left, (3) bottom, (4) right.

examples:

薬

"Grass" (kangxi #140) on top. "Tree" (kangxi #75) on bottom. So, two radicals, but you use the grass radical to look it up in a dictionary.

好

"Female" (kangxi #38) on left. "Child" (kangxi #39) on right. So, "female" is reference radical, but there still are two radicals.

薄

"Grass" (kangxi #140) radical on top. "Water" (kangxi #85) radical to left. Kangxi #41 ("thumb / inch") radical on bottom. So, the top radical is most important. The reference radical is "grass".

Organizing kanji is already difficult enough. Making a kanji such as 薄 referenceable by all 3 radicals would just be untenable. The (top / left / bottom / right) convention solves that problem. Of course, there are exceptions to the convention such as kangxi #163. Don't ever give-up until you look under kangxi #1.

Also, the number of strokes in a radical enhances its precedence... yes. it can be very frustrating using kanji dictionaries such as Nelson. People these days just use handwriting recognition. For example, one dark day I was brought to tears looking for "音". I kept referencing by the smaller radicals I saw. But in fact the whole kanji is a radical by itself. You've got my respect for using dictionaries instead of handwriting recognition!

Yes. When there is more than one radical, you first need to identify the primary radical. The convention is for the primary radical to be determined by its placement: (1) top, (2) left, (3) bottom, (4) right.

examples:

薬

"Grass" (kangxi #140) on top. "Tree" (kangxi #75) on bottom. So, two radicals, but you use the grass radical to look it up in a dictionary.

好

"Female" (kangxi #38) on left. "Child" (kangxi #39) on right. So, "female" is reference radical, but there still are two radicals.

薄

"Grass" (kangxi #140) radical on top. "Water" (kangxi #85) radical to left. Kangxi #41 ("thumb / inch") radical on bottom. So, the top radical is most important. The reference radical is "grass".

Organizing kanji is already difficult enough. Making a kanji such as 薄 referenceable by all 3 radicals would just be untenable. The (top / left / bottom / right) convention solves that problem. Of course, there are exceptions to the convention such as kangxi #163. Don't ever give-up until you look under kangxi #1.

Also, the number of strokes in a radical enhances its precedence... yes. it can be very frustrating using kanji dictionaries such as Nelson. People these days just use handwriting recognition. For example, one dark day I was brought to tears looking for "音". I kept referencing by the smaller radicals I saw. But in fact the whole kanji is a radical by itself. You've got my respect for using dictionaries instead of handwriting recognition!

final addendum
I just came across a perfect example of how radicals can drive you crazy:

意

The more complex radical (9 strokes) that is in the top position, 音, is somehow not the reference radical. Rather, it is the simpler radical on bottom, 心. You gotta love it.

Yes. When there is more than one radical, you first need to identify the primary radical. The convention is for the primary radical to be determined by its placement: (1) top, (2) left, (3) bottom, (4) right.

examples:

薬

"Grass" (kangxi #140) on top. "Tree" (kangxi #75) on bottom. So, two radicals, but you use the grass radical to look it up in a dictionary.

好

"Female" (kangxi #38) on left. "Child" (kangxi #39) on right. So, "female" is reference radical, but there still are two radicals.

薄

"Grass" (kangxi #140) radical on top. "Water" (kangxi #85) radical to left. Kangxi #41 (the "Sun"?) radical on bottom. So, the top radical is most important. The reference radical is "grass".

Organizing kanji is already difficult enough. Making a kanji such as 薄 referenceable by all 3 radicals would just be untenable. The (top / left / bottom / right) convention solves that problem. Of course, there are exceptions to the convention such as kangxi #163. Don't ever give-up until you look under kangxi #1.

Also, the number of strokes in a radical enhances its precedence... yes. it can be very frustrating using kanji dictionaries such as Nelson. People these days just use handwriting recognition. For example, one dark day I was brought to tears looking for "音". I kept referencing by the smaller radicals I saw. But in fact the whole kanji is a radical by itself. You've got my respect for using dictionaries instead of handwriting recognition!

Yes. When there is more than one radical, you first need to identify the primary radical. The convention is for the primary radical to be determined by its placement: (1) top, (2) left, (3) bottom, (4) right.

examples:

薬

"Grass" (kangxi #140) on top. "Tree" (kangxi #75) on bottom. So, two radicals, but you use the grass radical to look it up in a dictionary.

好

"Female" (kangxi #38) on left. "Child" (kangxi #39) on right. So, "female" is reference radical, but there still are two radicals.

薄

"Grass" (kangxi #140) radical on top. "Water" (kangxi #85) radical to left. Kangxi #41 (";thumb / inch";) radical on bottom. So, the top radical is most important. The reference radical is "grass".

Organizing kanji is already difficult enough. Making a kanji such as 薄 referenceable by all 3 radicals would just be untenable. The (top / left / bottom / right) convention solves that problem. Of course, there are exceptions to the convention such as kangxi #163. Don't ever give-up until you look under kangxi #1.

Also, the number of strokes in a radical enhances its precedence... yes. it can be very frustrating using kanji dictionaries such as Nelson. People these days just use handwriting recognition. For example, one dark day I was brought to tears looking for "音". I kept referencing by the smaller radicals I saw. But in fact the whole kanji is a radical by itself. You've got my respect for using dictionaries instead of handwriting recognition!

Yes. When there is more than one radical, you first need to identify the primary radical. The primary radical is determined by its placement: (1) top, (2) left, (3) bottom, (4) right.

examples:

薬

"Grass" (kangxi #140) on top. "Tree" (kangxi #75) on bottom. So, two radicals, but you use the grass radical to look it up in a dictionary.

好

"Female" (kangxi #38) on left. "Child" (kangxi #39) on right. So, "female" is reference radical, but there still are two radicals.

薄

"Grass" (kangxi #140) radical on top. "Water" (kangxi #85) radical to left. Kangxi #41 (the "Sun"?) radical on bottom. So, the top radical is most important. The reference radical is "grass".

Organizing kanji is already difficult enough. Making a kanji such as 薄 referenceable by all 3 radicals would just be untenable. The (top / left / bottom / right) rule solves that problem.

Also, the number of strokes in a radical enhances its precedence... yes. it can be very frustrating using kanji dictionaries such as Nelson. People these days just use handwriting recognition. For example, one dark day I was brought to tears looking for "音". I kept referencing by the smaller radicals I saw. But in fact the whole kanji is a radical by itself. You've got my respect for using dictionaries instead of handwriting recognition!

Yes. When there is more than one radical, you first need to identify the primary radical. The convention is for the primary radical to be determined by its placement: (1) top, (2) left, (3) bottom, (4) right.

examples:

薬

"Grass" (kangxi #140) on top. "Tree" (kangxi #75) on bottom. So, two radicals, but you use the grass radical to look it up in a dictionary.

好

"Female" (kangxi #38) on left. "Child" (kangxi #39) on right. So, "female" is reference radical, but there still are two radicals.

薄

"Grass" (kangxi #140) radical on top. "Water" (kangxi #85) radical to left. Kangxi #41 (the "Sun"?) radical on bottom. So, the top radical is most important. The reference radical is "grass".

Organizing kanji is already difficult enough. Making a kanji such as 薄 referenceable by all 3 radicals would just be untenable. The (top / left / bottom / right) convention solves that problem. Of course, there are exceptions to the convention such as kangxi #163. Don't ever give-up until you look under kangxi #1.

Also, the number of strokes in a radical enhances its precedence... yes. it can be very frustrating using kanji dictionaries such as Nelson. People these days just use handwriting recognition. For example, one dark day I was brought to tears looking for "音". I kept referencing by the smaller radicals I saw. But in fact the whole kanji is a radical by itself. You've got my respect for using dictionaries instead of handwriting recognition!