Dividing Radicals Calculator
Divide radical expressions with step-by-step solutions and simplified results
Divide Radical Expressions
First Radical (Dividend)
34√64
Second Radical (Divisor)
2√125
Division Result
0.1200√10
Simplified Form
≈ 0.379473
Decimal Approximation
Step-by-Step Solution
1.Original expression: (34√64) ÷ (2√125)
2.LCM of orders 4 and 2 is 4
3.Apply formula: (a / (c × d^(m-1))) × 4√(b^s × d^t)
4.Coefficient: 3 ÷ (2 × 125^1) = 0.0120
5.Radicand: 64^1 × 125^2 = 1000000
6.Simplified: 0.1200√10
General Formula: (a × ⁿ√b) ÷ (c × ᵐ√d) = (a ÷ (c × d^(m-1))) × ᵏ√(b^s × d^t)
Radical Properties
Quotient Rule
ⁿ√a ÷ ⁿ√b = ⁿ√(a/b)
Rationalization
Eliminate radicals from denominators
Simplification
Extract perfect powers from radicals
Quick Reference
•
Square Root
√a = a^(1/2)
•
Cube Root
³√a = a^(1/3)
•
nth Root
ⁿ√a = a^(1/n)
•
LCM Method
Find common denominator for division
Understanding Radical Division
What are Radicals?
Radicals (roots) are the inverse operations of exponents. The radical symbol √ indicates finding a number that, when raised to a certain power, gives the original number under the radical.
Division Process
- 1.Find the LCM of the radical orders
- 2.Apply the division formula
- 3.Simplify by extracting perfect powers
- 4.Reduce the radical order if possible
Division Formula
(a × ⁿ√b) ÷ (c × ᵐ√d) = (a / (c × d^(m-1))) × ᵏ√(b^s × d^t)
- k: LCM of n and m
- s: k / n
- t: k × (m - 1) / m
Common Examples
√8 ÷ √2 = √(8/2) = √4 = 2
6√12 ÷ 3√3 = 2√(12/3) = 2√4 = 4
³√16 ÷ √4 = ⁶√(16² × 4) = ⁶√1024 = 2√2