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Solving Equations with Radicals Test #1

In this Section:



In this section, we learn how to solve equations with radicals. Specifically, we will focus on how to solve equations with square roots. To accomplish this task, we introduce a new property of equality known as the: Squaring Property of Equality. The squaring property of equality has one hiccup. When we square both sides of an equation, the solution(s) of the original equation are among the solutions of the squared equation. This means a solution to the squared equation may or may not work in the original. For this reason, we must always check each and every solution in our original equation before we report our answer. So our steps are to isolate a square root, square both sides, and combine like terms. If there are any square roots left, we repeat this process until they are all gone. Then we solve the resulting equation and check all potential solutions.
Sections:

In this Section:



In this section, we learn how to solve equations with radicals. Specifically, we will focus on how to solve equations with square roots. To accomplish this task, we introduce a new property of equality known as the: Squaring Property of Equality. The squaring property of equality has one hiccup. When we square both sides of an equation, the solution(s) of the original equation are among the solutions of the squared equation. This means a solution to the squared equation may or may not work in the original. For this reason, we must always check each and every solution in our original equation before we report our answer. So our steps are to isolate a square root, square both sides, and combine like terms. If there are any square roots left, we repeat this process until they are all gone. Then we solve the resulting equation and check all potential solutions.