Radical equations

The  exercise appears under the Algebra I Math Mission. This exercise solves equations that are linear in "the square root of x."

Types of Problems
There is one type of problem in this exercise:


 * 1) Solve the radical equation: This problem has an equation that is linear except instead of x it has sqrt(x). The student is asked to solve the equation and select the answer from a multiple choice list.Radequ1.png

Strategies
Knowledge of solving linear equations and the ability to square numbers are the main skills required for success on this exercise.
 * 1) The equation is essentially of the form $$ax+b=cx+d$$, so the answer would almost be $$x=\frac{d-b}{a-c}$$. Here, this only solves for sqrt(x), so it is still necessary to square that answer.
 * 2) If the answer is found as described above, the squaring usually reasonable numbers to perform mentally.
 * 3) There is a possibility that there is no solution. The is recognizable immediately if $$d-b<0$$.

Real-life Applications

 * 1) Solving equations is an important skill in all classes beyond algebra.
 * 2) Radical equations occur when using approximations to find the height of a mountain using the curvature of the earth.