# How to write an expression in simplest radical form

Have them determine the side length for a square with an area of This is done by rationalizing the denominator.

Push them to explain why. The radicand has been reduced as much as possible. Then multiply both the numerator and denominator of the fraction by that square root and simplify.

Therefore we look for perfect square factors in the radicand. Here we want to go the other way. It sometimes happens that converting a product of roots to the root of a product produces a perfect square factor and that factor can then be removed from the radicand.

This is done by removing factors from the radical.

It is defined like this: Removing factors from the radicand Suppose that the index of the radical is n. I intentionally crafted these questions to be slightly different and an extension from those the students have just seen.

Have them determine the length of each side of the square. Have students turn and talk about what sqrt 25 actually means. I have them do a brief turn and talk to decide. The result is a radical in the numerator but none in the denominator. The result is a radical remaining in the numerator but none in the denominator.

The roots in this section have almost nothing to do with roots of an equation. The index, n, must be a positive integer. In each case, encourage students to find the "actual" answer using the calculator to see how close they are able to get with their estimate.

This means that for every property or rule that holds for an exponential there is a corresponding property or rule for a radical. Encourage students to make a hypothesis about how to simplify the expression, test their hypothesis, and revise if needed.

Eliminate the radical from the denominator of the expression. By thinking about "nearby" radicals that simplify to whole numbers, students can get a decent approximation as to the quantity that a radical expression represents.

Combining products of radicals We saw above that the root of a product could be rewritten as a product of roots. See the first example above.

Slide 1 Now that students are beginning to understand that you can take the square root of "non-perfect squares", we want to talk more about estimating. Here are the steps:When we multiply and divide radical expressions, we need to 1) Rewrite the radical expressions in exponential form (using fractions for exponents, if necessary).

2) Make sure the bases are the same. If they aren’t, then take action to get them to be the same numbers (are they powers of the same number?). A fraction in its simplest form has to have a positive denominator.

To turn a negative denominator into a positive, multiply both parts of the fraction by in other words, it represents a negative quantity. As long as you write only one negative sign, it doesn't matter whether you put it before the denominator, before the numerator or.

In mathematics, a radical expression is defined as any expression containing a radical (√) symbol - includes square roots, cube roots and so forth. Expressing in simplest radical form just means simplifying a radical so that there are no more square roots, cube roots, 4th roots, etc left to find.

This radical expression has been denoted in the root symbol $\sqrt{}$. Thus the process to simplify a radical is to write it in simplest form possible. To simplify a radical the first step is check if the radicand is a multiple of any perfect square, and then to take that perfect square out of the radical.

Illustrated definition of Simplest Form (Algebra): In general, an expression is in simplest form when it is easiest to use. Example, this: 5x x minus 3 Is.

Algebra II Recipe: Changing Exponential Form to Radical Form: Introduction: A. Given. The numerator (1) is the power. The denominator (2) is the root. Radical form: B. Given Radical form = Practice Problems. G Redden: Show Related AlgebraLab Documents: AlgebraLAB Project Manager Catharine H. .

How to write an expression in simplest radical form
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