Summary: Simplifying and Using Square Roots

Key Concepts

  • Square Root Notation [latex]\sqrt{m}[/latex] is read ‘the square root of [latex]m[/latex] ’.  If [latex]m={n}^{2}[/latex] , then [latex]\sqrt{m}=n[/latex] , for [latex]n\ge 0[/latex] .
    When taking the square root, the number inside the radical sign is called the radicand
  • Square Roots and Area If the area of the square is A square units, the length of a side is [latex]\sqrt{A}[/latex] units.
  • Square Roots and Gravity On Earth, if an object is dropped from a height of [latex]h[/latex] feet, the time in seconds it will take to reach the ground is found by evaluating the expression [latex]{\Large\frac{\sqrt{h}}{4}}[/latex].
  • Square Roots and Accident Investigations Police officers investigating car accidents measure the length of the skid marks on the pavement. Then they use square roots to determine the speed, in miles per hour, a car was going before applying the brakes. According to some formulas, if the length of the skid marks is [latex]d[/latex] feet, then the speed of the car can be found by evaluating [latex]\sqrt{24d}[/latex].
  • Use a strategy for applications with square roots.
    • Identify what you are asked to find.
    • Write a phrase that gives the information to find it.
    • Translate the phrase to an expression.
    • Simplify the expression.
    • Write a complete sentence that answers the question.


Perfect square
A perfect square is the square of a whole number.
Square Root of a Number
A number whose square is [latex]m[/latex] is called a square root of [latex]m[/latex].
If [latex]{n}^{2}=m[/latex], then [latex]n[/latex] is a square root of [latex]m[/latex].