Simplify Radicals Calculator
How It Works
This simplify radicals calculator uses established formulas to provide accurate results.
The basic rule:
- √(a·b) = √a · √b
- Find largest perfect square factor
- √n = c√r where c² · r = n
Results are estimates. Consult a professional for critical decisions.
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Explore Allday Everyday Math →Frequently Asked Questions
How do I simplify a square root?
Find the largest perfect square that divides the radicand. Factor it out, take its square root, and leave the rest under the radical. For example, √72 = √(36·2) = 6√2.
What is a perfect square?
A perfect square is a number that is the square of an integer: 1, 4, 9, 16, 25, 36, 49, 64, 81, 100, etc. When simplifying, look for the largest perfect square factor.
When is a radical fully simplified?
A radical is fully simplified when no perfect square factor (other than 1) remains under the radical sign. For example, √12 is not simplified (contains factor 4), but 2√3 is.
Can you simplify √2?
No. Since 2 has no perfect square factors other than 1, √2 is already in simplest radical form. It is an irrational number approximately equal to 1.414.