Any good libre replacement for Wolfram Alpha?

I was expected to use something like Wolfram Alpha to find the exact root

I teach numerical analysis. Starting the chapter on root finding, I say: "raise your hand if you can solve x² = 2". Most of the students do. I ask one of them: "what is the positive solution of x² = 2 then?". He or she answers "the square root of 2". However, what is a square root of a number a? By definition, it is the positive number that, squared, equals a. So answering that the positive solution of x² = 2 is the square root of 2 is just repeating the question. It is not solving the equation. In Maxima, solve gives the same disappointing solution:
$ maxima
Maxima 5.41.0 http://maxima.sourceforge.net
using Lisp GNU Common Lisp (GCL) GCL 2.6.12
Distributed under the GNU Public License. See the file COPYING.
Dedicated to the memory of William Schelter.
The function bug_report() provides bug reporting information.
(%i1) solve(x^2 = 2);
(%o1) [x = - sqrt(2), x = sqrt(2)]
To really solve that equation, you need a root finding algorithm, after bracketing the root of interest, here between 1 and 2:
(%i2) find_root(x^2 = 2, x, 1, 2);
(%o2) 1.414213562373095
Here is a solution! Not repeating the problem! The solution is not exact indeed. The actual solution is an irrational number, with infinite decimals that never enter a cycle. We can get more decimals increasing the number of bits in the mantissa of the representations of the numbers in floating-point algorithmic, if the programming language natively allows it. We can even use a library that implements arbitrary precision arithmetic (at a high computational cost, compared to using a native type such as "double"), like GNU MP (for C or C++) or Boost (only for C++). Maxima, which is not used in applications such as numerical simulations where performance matters, has bf_find_root (where "bf" stands for "bigfloat"):
(%i3) bf_find_root(x^2 = 2, x, 1, 2);
(%o3) 1.414213562373095048801688724209698078569671875376948073176679738b0
We will never get the infinite decimals, the exact solution. They do not fit in the universe. But no real-world application needs the infinite decimals. Also, even if solutions expressed with square/cubic/... roots are considered acceptable, most of the equations cannot have their roots expressed in this way. Even the roots of an algebraic equation of degree 5 or more cannot, in the general case, be expressed in this way (a result from group theory). Numerical analysis is needed.