Dividing radicals combines them under one root and then removes the root from the denominator (rationalising), which is the conventional simplest form.
How to use the Dividing Radicals Calculator
- Operation
- a (coefficient)
- b (radicand)
- n (index)
- c (coefficient)
- d (radicand)
- m (index)
Everything is calculated in your browser, so results appear instantly and nothing you type is sent to a server.
How it works
Enter both radicals. The calculator brings them to a common index, multiplies top and bottom by the radical needed to clear the denominator, and simplifies.
Formula
(a·ⁿ√b) / (c·ᵐ√d) = (a/c) · ᵏ√(b^(k/n) / d^(k/m)), k = LCM(n, m)
Worked example
Inputs — Operation: Divide; a (coefficient): 6; b (radicand): 10; n (index): 2; c (coefficient): 2; d (radicand): 5; m (index): 2.
Results — Result = 3√2; Decimal value = 4.242640687; Steps = Multiply top and bottom by √5 to clear the root from the denominator, then simplify..
Key terms
- Rationalise
- Remove radicals from a denominator.
Frequently asked questions
What is √50 ÷ √2?
√25 = 5.
Why rationalise the denominator?
It is the conventional simplest form and makes values easier to compare.
How do I divide radicals with different indices?
Rewrite them with a common index first.
What is 1/√2 rationalised?
√2/2.