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How to Reduce a Square Root

A square root is a value that, when multiplied times itself, equals another specific value. Square roots can consist of a combination of numbers, letters and exponents. You are likely to encounter assignments involving square roots in high school and college algebra and calculus courses. Reducing a square root means to break down the expression into its simplest terms. You can easily do this by following rules that apply to square root calculations.

Instructions

    • 1

      Solve simple square roots by determining which number multiplied times itself equals the number under the square root symbol. For example, the square root of 100 is 10, since 10 times 10 equals 100. If you have a variable that is squared under the radical sign, you can simply extract the variable. For instance, the square root of x^2 is x.

    • 2

      Reduce a radicand (number under the radical symbol) to its factors and look for perfect squares. For example, if you have √8, break this into √4 * √2. Factor out 2, since it is the square root of 4, leaving you with the answer 2√2.

    • 3

      Reduce a fraction with a square root in the denominator by multiplying the numerator and the denominator by the square root given. For example, if you have 2/â??3, multiply both numbers by â??3 to get 2â??3/3.

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