The search for a specific "write-up" or answer key for (Решение ГИА Алгебра 8 класс Воронина О.А.) suggests a request for a solution manual or study guide for a 8th-grade Algebra workbook focused on the State Final Examination (GIA) format.

Properties of arithmetic square roots and irrational numbers.

This is the most comprehensive source for GIA-style (and VPR) algebra problems. You can find thousands of tasks for 8th-grade math, including step-by-step solutions for number inequalities, rational expressions, and equations at the Math 8 SDAM GIA Portal .

Solving using the discriminant and Vieta's theorem.

Simplifying fractions, addition, subtraction, and multiplication of rational expressions.

For general 8th-grade Algebra textbooks (like Makarychev or Mordkovich which these test books often follow), Skysmart provides verified solutions and explanations.