How to Simplify Radicals for Higher Algebra, Step by Step


In math, when the same number is multiplied together many times, this is known as a power operation. For example, if you multiply 2 by itself twice, then this can be written as 2 to the power of 2 (2^2), and the result is equal to 4. The inverse operation can be applied by obtaining the "root" or the radical. For example, the radical (or square root) of 4 reverses the power operation, yielding 2. Radicals can be simplified using a set of straightforward mathematical rules.

Things You'll Need

  • Pen
  • Paper
  • Write out the rules for radicals. The product rule states that two radicals can be multiplied together if they have the same root:

    n√a x n√b = n√ab

    The quotient rule states that two radicals can be divided if they have the same root:

    n√a / n√b = n√(a/b)

    These rules apply to numbers as well as algebraic expressions.

  • Write down the radical that needs to be simplified. For the sake of this example, let's assume that the radical is an algebraic expression: 2√(4a^3).

  • Use the product and quotient rules to split the radical into simpler components. Following the example, 2√(4a^3) can be written as a product:

    2√(4a^3) = 2√(4 x a x a^2) = 2√4 x 2√(a^2) x 2√a

  • Evaluate as many terms as possible within the product. Following the example, we know that the radical of 4 is equal to 2 and that the radical of a-squared is equal to a:

    2√4 x 2√(a^2) x 2√a = 4 x 2a x (2√a)


  • Photo Credit Zoonar RF/Zoonar/Getty Images
Promoted By Zergnet



You May Also Like

  • How to Solve Radical Equations

    Radical equations are equations with a square root on either of their sides. For example, sqrt(x + 1) + 6 = 9...

  • How to Simplify Square Roots (Radicals)

    A common task in algebra is to simplify square roots, or what are referred to in later math as radicals. This article...

  • How to Simplify Polynomials

    Algebra revolves around polynomials, especially the quadratic equation. To be a polynomial, each term must have only whole number exponents on its...

  • How to Simplify Radicals

    A radical is denoted by a mathematical symbol that looks a bit like a check mark (?). Numbers are placed inside the...

  • What Are Radicals in Math?

    A radical, or root, is the mathematical opposite of an exponent, in the same sense that addition is the opposite of subtraction....

  • How to Multiply a Radical by a Number

    Multiplying a radical by a number can be accomplished by following a few basic steps. Multiply a radical by a number with...

Related Searches

Check It Out

How to Build and Grow a Salad Garden On Your Balcony

Is DIY in your DNA? Become part of our maker community.
Submit Your Work!