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I'm trying to build a program that let's you multiply two square roots and display the answer in surd form if the answer isn't an integer.

I've seen answers here and here, although I don't understand C++ and C#, so I don't have a clue on what to do. The first thing I've done is multiply the two numbers inside the square roots together, then I can display the answer if it is an integer, but if it isn't it completely messes up.

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  • can you show us your code? Commented Jun 22, 2022 at 19:43
  • just multiply the no normaly, make the prime factors of it, and than take sqaure root on them, any other no left will be inside square root Commented Jun 22, 2022 at 19:45
  • (Surd (mathematics), an unresolved root or sum of roots) Commented Jun 23, 2022 at 5:35

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I don't see a better way than by factoring the given numbers, summing the multiplicities of the prime factors, extracting the even parts of the multiplicities and forming the square root of the products.

E.g.

√(84.375)=√(2²3.7.3.5³)=√(2²3²5³7)=2.3.5√(5.7)=30√35
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7 Comments

There is a better way. If you're multiplying two square-free surds, the GCD is going to be the integer. That can be calculated by the Euclidean algorithm without any factoring required.
@btilly: can you explain how you exploit that to solve the given problem ?
If the numbers are pairs [a, b] representing a sqrt(b) then [a, b] times [c, d] is [ac + gcd(b, d), bd / gcd(bd)^2]. It doesn't help if you start with them not in that form though.
@btilly: ok, I missed that the numbers could be given in surd form. (Then every factor of the root part has exactly multiplicity one, and common factors get multiplicity two.) Would you like to enter an answer, or shall I update mine ?
I'm not, rereading the question, positive that they could be given in surd form.
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Try using SymPy:

>>>import sympy >>>sympy.sqrt(8) 2*sqrt(2)
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