Equations with square roots and cube roots

The  exercise appears under the 8th grade (U.S.) Math Mission. This exercise solves equations and works with problems that involve radicals.

Types of Problems
There are two types of problems in this exercise:


 * 1) Select equations with a given solution: This problem provides a possible solution to an equation. The student is asked to select the equations that have that number as a solution from a multiple select list.Ewsracr1.png
 * 2) Find the error in reasoning: This problem provides the step-by-step solution to a problem involving a radical. The student is asked to find the precise step where an error occurred in the solution, or to indicate that no error was made.Ewsracr2.png

Strategies
Knowledge of radicals and powers of numbers are encouraged to ensure success on this exercise.
 * 1) The square root of a number (principal root) is always positive.
 * 2) The square root property states that if $$x^2=a^2$$ then $$x=\pm a $$.
 * 3) Generally (at this stage) odd index radicals only have one solution, whereas even index radicals have two.
 * 4) On Find the error in reasoning, if the final answer is correct than the steps in the process were correct. This fact can increase efficiency on this problem.

Real-life Applications

 * 1) Radicals can appear in equations in physics, for example, the force of gravity between two objects.
 * 2) Equations with integer powers can require radicals to be solved.
 * 3) An ability to troubleshoot and find errors is valuable in almost any field.