It's a tough one, but I think cassava is the one English speaking people will be most familiar with.

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Note added at 2002-01-21 00:35:40 (GMT)
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I hadn\'t thought there might be a difference between Mandioca and mandioquinha. I stand corrected.

...also exists, but I prefer cassava

You can probably get by with cassava, but as I recall from several years of living in Brazil, mandioquinha is not the same as manioca. (manioc/cassava). I was hoping that my trusty old Taylor dictionary would give a translation, because he's usually good with flora and fauna. All I could find were references in Aurelio referring me to "batata-baroa" and "bucho de boi" - said to be synonyms. Here are the two references:

Planta da família das umbelíferas (Arracacia xanthorrhiza), originária dos Andes e largamente cultivada em toda a América do Sul. É erva robusta, com grandes raízes amarelas, utilizada na alimentação do homem e como forragem.

Árvore da família das bignoniáceas (Zeyheria tuberculosa), de flores amarelas manchadas de púrpura, fruto capsular e madeira usada para construção civil.

Perhaps someone else will come up with a better suggestion,

Check these links. I simply placed the scientific name in Google and got a bunch of references. These were the most complete one.

Good luck. Gio

Mandioca and mandioquinha are two different edible roots/tubers.
Mandioquinha ou batata-baroa (S. f.) - Planta da família das umbelíferas (Arracacia xanthorrhiza), originária dos Andes e largamente cultivada em toda a América do Sul. É erva robusta, com grandes raízes amarelas, utilizada na alimentação do homem e como forragem. Também conhecida como: batata-cenoura, arracachá, mandioca-baroa, mandioquinha.
Mandioca (S. f. Bras.) - Planta leitosa, da família das euforbiáceas (Manihot utilíssima), cujos grossos tubérculos radiculares, ricos em amido, são de largo emprego na alimentação, e da qual há espécies venenosas, que servem para fazer farinha de mesa.

A Google search for the latin names led to:
Arracacia xanthorrhiza - sin. Arracacia esculenta; sin. Conium arracacha
According to Purdue Univ.: apio, arracach, arracacha, arracacia, fecula, Peruvian carrot, Peruvian parsnip, r'accacha, white carrot;
http://www.hort.purdue.edu/newcrop/nexus/Arracacia_xanthorrh...
According to Univ. of Idaho: white carrot; arracacha; Peruvian-carrot; pomme-de-terre-celeri;
http://image.fs.uidaho.edu/vide/famly134.htm

Manihot esculenta (syn. Jatropha dulcis; Jatropha manihot; Manihot aipi; Manihot dulcis; Manihot manihot; Manihot melanobasis; Manihot utilissima)
Cassava; Manioc; Yuca; Tapioca-plant
http://image.fs.uidaho.edu/vide/famly058.htm


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Note added at 2002-01-20 20:49:51 (GMT)
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Peruvian parsnip is the correct suggestion, as parsnip alone corresponds to Pastinaca sativa, which was brought from Europe to USA in the early 1600.

Mandioquinha has nothing to do with mandioca, except for the fact that they kind of look alike, despite the size difference. The coloquial name in English is white carrot, but since very few people will have heard of white carrot, I would be creative and say
mandioquinha (or little cassava) soup.
Tomara que ajude!

A root that can be transformed in a nutritional food and a variety of food as tapioca.

Peruvian parsnip or peruvian carrot may be used, but they may sound just as foreign as "mandioquinha" itself. I suggest using "mandioquinha" with a footnote containing a brief explanation on what it is, its english name, and pointing out that it is not the same as cassava or manioc.