Solve square-root equations (advanced)

The  exercise appears under the Algebra II Math Mission. This exercise practices solving square-root equations by taking the square of both sides.

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


 * 1) Fill in the blanks with the solution(s) of the equation: This problem asks has a square root equation with a variable. Student are expected to solve for the variable and type the solutions(s) in the space provided. Solve square-root equations (advanced).PNG

Strategies
Knowledge of square root equations are needed to do this exercise accurately and correctly.
 * 1) If the equation contains two radicals, but that each radical is completely isolated on opposite sides of the equation, users can therefore square both sides to eliminate the radical terms.
 * 2) If there are two such solutions, users need to enter them in ascending order.
 * 3) If there is only one such solution, users need to leave the second blank empty.
 * 4) If there are zero such solutions, users need to leave both blanks empty.

Real-life applications

 * 1) Square roots have many uses in the physics as they are the way to undo squares in famous formulas like $$E=mc^2$$.
 * 2) Applications to trigonometry are also evident since the right triangle trigonometry is based on the Pythagorean Theorem.
 * 3) In geometry, the square root is necessary to find the distance between points or the magnitude of a vector.