Using a mandolin or very sharp knife, julienne the jicama, beets, and carrots and combine in a large bowl.
Slice off the ends of the oranges. Using a paring knife, remove the peel and pith from the oranges, following the curve of the fruit. Slice on either side of the membranes to remove the segments. Transfer the orange segments to the jicama mixture.
Squeeze enough juice from the membranes into a bowl, to make 1/4 cup. Whisk the lime juice into the orange juice. While whisking, drizzle in the oil to make smooth vinaigrette. Pour the vinaigrette over jicama mixture, toss to coat, and season with salt and pepper.
Transfer the jicama salad to a platter and sprinkle with the peanuts.