Simplify Radicals Calculator: Your Guide to Square Root Simplification
ByMuhammad Ali•Founder of KruskalCode
07:52
6 min read
Simplifying radicals is a fundamental skill in algebra, often encountered in high school mathematics. It involves rewriting a square root expression so that the radicand (the number under the radical symbol) has no perfect square factors other than 1. This makes expressions easier to work with and understand. Our Simplify Radicals Calculator is designed to help you master this process quickly and accurately.
Explanation
A radical expression is in its simplest form when the radicand contains no perfect square factors. For example, √12 is not simplified because 4 (a perfect square) is a factor of 12. We can rewrite √12 as √(4 × 3), which simplifies to 2√3. The goal is to extract as many perfect square factors as possible from the radicand. This often involves prime factorization to identify pairs of factors that can be 'taken out' of the square root.
Formula
The general formula for simplifying a square root is: √A = √(B² × C) = B√C Where A is the original radicand, B² is the largest perfect square factor of A, and C is the remaining factor. If A has no perfect square factors other than 1, then A is already in its simplest form.
Example
Let's simplify √98 using the steps: 1. **Find the prime factorization of 98:** 98 = 2 × 49 = 2 × 7 × 7. 2. **Identify pairs of factors:** We have a pair of 7s (7 × 7). 3. **Extract perfect squares:** Since 7 × 7 = 49 (a perfect square), we can take one 7 out of the radical. 4. **Remaining factors:** The factor 2 remains inside the radical. 5. **Write the simplified form:** Therefore, √98 simplifies to 7√2.
How to use the related calculator
Using the Simplify Radicals Calculator is straightforward. Simply enter the positive integer you wish to simplify into the 'Radicand' input field. For instance, if you want to simplify √72, type '72'. Click the 'Calculate' button, and the tool will instantly display the simplified radical form, such as '6√2'. The calculator handles the prime factorization and grouping for you, making complex simplifications easy.
Try the related calculator
Open toolFAQ
What is a radicand?
A radicand is the number or expression under the radical symbol (√). For example, in √25, 25 is the radicand.
Why is it important to simplify radicals?
Simplifying radicals makes expressions easier to understand, compare, and perform further calculations with. It's a standard practice in algebra to present radical expressions in their simplest form.
Can I use this calculator for cube roots or other roots?
No, this specific calculator is designed to simplify square roots only. For other types of roots, you would need a different approach or a specialized tool.
What if the radicand is a prime number?
If the radicand is a prime number (like 7, 11, 13), it has no perfect square factors other than 1. In such cases, the radical is already in its simplest form and cannot be simplified further.
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About the author
Muhammad Ali. Muhammad Ali is a full-stack developer and founder of KruskalCode. He builds SaaS platforms and automation systems with React and Laravel, and helps teams ship fast, scalable tools.
Need a custom calculator, dashboard, or automation workflow? Reach out to KruskalCode.
