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You may find Math Stackexchange helpful. Dr. Math also likely has something in their archives.

However, this forum is specifically for asking how to do things with Sage mathematics software. We can compute radicals of ideals, which could conceivably help you gain intuition:

sage: P.<x,y,z> = QQ[]
sage: I = Ideal(x+y+z-3,x^2+y^2+z^2-5,x^3+y^3+z^3-7)
sage: I.radical()
Ideal (x + y + z - 3, y^2 + y*z + z^2 - 3*y - 3*z + 2, 3*z^3 - 9*z^2 + 6*z + 2) of Multivariate Polynomial Ring in x, y, z over Rational Field

However, using such forums for homework help is a breach of netiquette - see the FAQ (which has a typo in one of the first lines... sigh).