This online Simplifying Radical Expressions Calculator finds a simplified form of the given radical expression of the general form a⋅ⁿ√b. The radicand is to be an integer number between 2 and 2⁵³ – 1 = 9007199254740991. Enter the values of the radicand b and integer index n (factor a is optional) in the input fields of the calculator and click the ‘Calculate’ button to get the result.
a·n√b
Simplifying Radical Expressions
Simplifying radical expressions refers to the process of rewriting a radical expression in its simplest form without changing its value. In mathematics, a radical typically involves a root, such as a square root (√), cube root (∛), or more generally the n-th root (ⁿ√). Simplification often involves removing radicals from the denominator, factoring out perfect powers, and expressing the result in the most reduced form possible.
The goal of simplification is to make radical expressions easier to understand, compare, and use in further calculations. A simplified radical expression is more concise, which is especially useful in algebra, geometry, trigonometry, and various applied sciences.
Definition and Overview
A radical expression usually takes the form:
$$ a\cdot \sqrt[n]{b}$$
where:
• \(a\) is a coefficient,
• \(n\) is the index of the radical (with 2 implying a square root),
• \(b\) is the radicand (the value under the root symbol).
Simplifying a radical expression generally means:
- Factoring the radicand to find and extract any perfect powers of \(n\),
- Rationalizing the denominator (if the radical appears in the denominator),
- Combining like terms when possible.
Examples of Simplified vs. Un-simplified Forms
For example, un-simplified form of a radical 2√18 can be reduced to the simplified one: 6√2 (because 2√18 = 2√(9×2) = 2√9·√2 = 2·3√2 = 6√2).
Let’s walk through a more detailed example of simplifying the radical expression: √72
Step 1. Factor the radicand into two factors: 72 = 36 × 2
Step 2. Identify perfect squares (in our case 36): √72 = √(36×2) = √36 × √2 = 6√2
The final result is: 6√2
Simplifying radical expressions is an important component of math that enhances both understanding and usability of mathematical formulas. By expressing radicals in their simplest form, calculations become more straightforward, errors are minimized, and consistency is maintained. Our Simplifying Radical Expressions Calculator allows you to easily perform these calculations in a fraction of a second.
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