Mathematics » Roots and Radicals » Solve Equations with Square Roots

Solving Equations With Square Roots Summary

Key Concepts

  • To Solve a Radical Equation:
    1. Isolate the radical on one side of the equation.
    2. Square both sides of the equation.
    3. Solve the new equation.
    4. Check the answer. Some solutions obtained may not work in the original equation.
  • Solving Applications with Formulas
    1. Read the problem and make sure all the words and ideas are understood. When appropriate, draw a figure and label it with the given information.
    2. Identify what we are looking for.
    3. Name what we are looking for by choosing a variable to represent it.
    4. Translate into an equation by writing the appropriate formula or model for the situation. Substitute in the given information.
    5. Solve the equation using good algebra techniques.
    6. Check the answer in the problem and make sure it makes sense.
    7. Answer the question with a complete sentence.
  • Area of a Square
    This figure shows a square with two sides labeled, “s.” The figure also says, “Area, A,” “A equals s squared,” “Lenth of a side, s,” and “s equals the square root of A.”
  • Falling Objects
    • On Earth, if an object is dropped from a height of \(h\) feet, the time in seconds it will take to reach the ground is found by using the formula \(t=\frac{\sqrt{h}}{4}\).
  • Skid Marks and Speed of a Car
    • If the length of the skid marks is d feet, then the speed, s, of the car before the brakes were applied can be found by using the formula \(s=\sqrt{24d}\).


radical equation

An equation in which the variable is in the radicand of a square root is called a radical equation

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