def test_nthroot1():
q = 1 + sqrt(2) + sqrt(3) + S(1) / 10**20
p = expand_multinomial(q**5)
assert nthroot(p, 5) == q
q = 1 + sqrt(2) + sqrt(3) + S(1) / 10**30
p = expand_multinomial(q**5)
assert nthroot(p, 5) == q
def test_nthroot1():
q = 1 + sqrt(2) + sqrt(3) + S(1)/10**20
p = expand_multinomial(q**5)
assert nthroot(p, 5) == q
q = 1 + sqrt(2) + sqrt(3) + S(1)/10**30
p = expand_multinomial(q**5)
assert nthroot(p, 5) == q
def test_nthroot():
assert nthroot(90 + 34 * sqrt(7), 3) == sqrt(7) + 3
q = 1 + sqrt(2) - 2 * sqrt(3) + sqrt(6) + sqrt(7)
assert nthroot(expand_multinomial(q**3), 3) == q
assert nthroot(41 + 29 * sqrt(2), 5) == 1 + sqrt(2)
assert nthroot(-41 - 29 * sqrt(2), 5) == -1 - sqrt(2)
expr = 1320 * sqrt(10) + 4216 + 2576 * sqrt(6) + 1640 * sqrt(15)
assert nthroot(expr, 5) == 1 + sqrt(6) + sqrt(15)
q = 1 + sqrt(2) + sqrt(3) + sqrt(5)
assert expand_multinomial(nthroot(expand_multinomial(q**5), 5)) == q
q = 1 + sqrt(2) + 7 * sqrt(6) + 2 * sqrt(10)
assert nthroot(expand_multinomial(q**5), 5, 8) == q
q = 1 + sqrt(2) - 2 * sqrt(3) + 1171 * sqrt(6)
assert nthroot(expand_multinomial(q**3), 3) == q
assert nthroot(expand_multinomial(q**6), 6) == q
def test_nthroot():
assert nthroot(90 + 34*sqrt(7), 3) == sqrt(7) + 3
q = 1 + sqrt(2) - 2*sqrt(3) + sqrt(6) + sqrt(7)
assert nthroot(expand_multinomial(q**3), 3) == q
assert nthroot(41 + 29*sqrt(2), 5) == 1 + sqrt(2)
assert nthroot(-41 - 29*sqrt(2), 5) == -1 - sqrt(2)
expr = 1320*sqrt(10) + 4216 + 2576*sqrt(6) + 1640*sqrt(15)
assert nthroot(expr, 5) == 1 + sqrt(6) + sqrt(15)
q = 1 + sqrt(2) + sqrt(3) + sqrt(5)
assert expand_multinomial(nthroot(expand_multinomial(q**5), 5)) == q
q = 1 + sqrt(2) + 7*sqrt(6) + 2*sqrt(10)
assert nthroot(expand_multinomial(q**5), 5, 8) == q
q = 1 + sqrt(2) - 2*sqrt(3) + 1171*sqrt(6)
assert nthroot(expand_multinomial(q**3), 3) == q
assert nthroot(expand_multinomial(q**6), 6) == q