Apply the quotient property of radicals: √(a) / √(b) = √(a/b).
Last updated: March 2026 | By ForgeCalc Engineering
The quotient property of radicals states that the square root of a quotient is equal to the quotient of the square roots. In other words, you can combine two square roots being divided into a single square root of the division of their radicands.
When coefficients are present, you divide the coefficients separately from the radicals. If the resulting radical can be simplified further, it should be.
For coefficients: (m√a) / (n√b) = (m/n)√(a/b).
Divide 12√6 by 2√3:
1. Divide coefficients: 12 / 2 = 6
2. Divide radicands: √(6 / 3) = √2
3. Combine: 6√2
Final Answer: 6√2 (≈ 8.4853)
It's the process of removing a radical from the denominator of a fraction by multiplying the numerator and denominator by an appropriate value.
Not directly using this property. You must first convert them to have a common index using fractional exponents.
For square roots, a negative radicand results in an imaginary number. This calculator assumes positive real numbers for radicands.
Yes! The property $sqrt[n]{a} / sqrt[n]{b} = sqrt[n]{a/b}$ works for any index $n$.
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