Astute rhymes with:
toot, toote, tuite, absolut, acute, beabout, bebout, beirut, bluett, bluitt, boot, boote, boutte, brut, brute, bute, butte, cahoot, cahouet, caillouet, caouette, chute, clute, commute, compute, coot, coote, crute, cute, degroote, dilute, dispute, disrepute, enroute, fluet, flute, fruit, garoutte, grassroot, groot, hirsute, hoot, huett, huette, huitt, impute, juett, jute, klute, knute, loot, lute, macoute, moot, mute, newt, nute, permute, pollute, pruett, puett, pursuit, pute, recruit, refute, repute, reroute, root, route, salute, schuett, schuette, scoot, shoot, shute, smoot, stroot, subacute, suit, suitt, toot, toote, truett, truitt, tuite, undilute, uproot, voute, zoot-suit
Astute sounds like:
acadia, accede, acceded, accessed, accetta, accost, accosted, accused, aced, acetate, aceto, ached, acid, acidity, acosta, acott, acquiesced, acquit, acquitted, act, acted, actuate, acuity, acusyst, acute, aesthete, agate, agatha, aged, aghast, aghazadeh, agitate, agitated, agosta, agosto, aguacate, aguado, aist, ajito, akihito, akita, akst, aqazadeh, asat, asato, ascot, ascott, asda, ashwood, aside, asked, asquith, assad, assed, assessed, asset, assist, assisted, associate, associated, assuaged, ast, asta, aucott, augat, august, augusta, auguste, augusto, aust, austad, austat, axed, axid, axt, azzato