How do you write a radical in simplest form

Example 2 — Simplify: Step 1: Find the prime factorization of the number inside the radical and factor each variable inside the radical.

square root of 15 in radical form

In this example, the largest factor that both numbers have in common is 2. But there are other ways in which a fraction can become complicated. To simplify radicals, rather than looking for perfect squares or perfect cubes within a number or a variable the way it is shown in most books, I choose to do the problems a different way, and here is how.

simplifying radical expressions

Or, to put it another way, you'll get the same result if you flip that second fraction upside down creating the inverse and multiply by that, which is a much easier operation to perform.

For example, if the index is 2 a square rootthen you need two of a kind to move from inside the radical to outside the radical. If the index is 3 a cube rootthen you need three of a kind to move from inside the radical to outside the radical.

square root of 14 in radical form

Simplifying Complex Fractions Another common obstacle you might encounter to writing a fraction in its simplest form is a complex fraction — that is, a fraction that has another fraction in either its numerator or its denominator, or both. Step 2: Determine the index of the radical.

Square root of 14 in radical form

Its value hasn't changed; only the way you write it has changed. In this case, the index is four because it is a fourth root, which means we need four of a kind. Then divide by 3, 5, 7, etc. In this case, the index is three because it is a cube root, which means we need three of a kind. Step 3: Move each group of numbers or variables from inside the radical to outside the radical. Simplifying Complex Fractions Another common obstacle you might encounter to writing a fraction in its simplest form is a complex fraction — that is, a fraction that has another fraction in either its numerator or its denominator, or both. Click Here for Practice Problems Example 3 — Simplify: Step 1: Find the prime factorization of the number inside the radical and factor each variable inside the radical.
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Simplest Radical Form