Divide Radicals Calculator
Divide radical expressions with automatic rationalization and step-by-step solutions
Dividing Radicals
When dividing radicals, divide the coefficients and radicands separately. The quotient property states: √a ÷ √b = √(a/b). Always simplify and rationalize denominators when needed.
Frequently Asked Questions
How do you divide radicals?
Divide the coefficients and radicands separately, then simplify the result. Use the quotient property: √a ÷ √b = √(a/b).
What is the quotient property of radicals?
The quotient property states that the quotient of two radicals equals the radical of the quotient: ⁿ√a ÷ ⁿ√b = ⁿ√(a/b), provided both radicals have the same index.
Do you need to rationalize after dividing?
Yes, if the result has a radical in the denominator, you should rationalize it by multiplying both numerator and denominator by an appropriate radical.
Can you divide radicals with different indices?
No, you cannot directly divide radicals with different indices using the quotient property. Convert them to exponential form first.
What if the radicands are the same?
If the radicands are the same, they cancel out: √a ÷ √a = 1. You're left with just the quotient of the coefficients.
How do you simplify after dividing?
First divide to get the quotient, then look for perfect square factors (or perfect nth power factors) that can be simplified out of the radical.