Comprehensive Calculator Guide
This calculator puts any radical in simplest form by taking factors out from under the root, for square roots, cube roots and higher. √72 = 6√2, ∛54 = 3∛2 and √200 = 10√2. It shows what comes out, what stays inside, the prime factors and the decimal value.
How to simplify
Factor the radicand into primes; for a square root take one factor out for each pair, for a cube root one for each triple. Simplified radicals can then be added: √72 + √8 = 6√2 + 2√2 = 8√2.
How to Use
- Enter the radicand.
- Enter the index: 2 for square, 3 for cube.
- Press “Simplify” to see the simplest form.
Formula Used
ⁿ√(aⁿ × b) = a × ⁿ√b
Practical Examples
- Example 1: √72
- 6√2.
- Example 2: ∛54
- 3∛2.
- Example 3: √200
- 10√2.
Important Tips
- Try the largest perfect square you know first.
- Check by multiplying back.
- Simplify before adding.
Common Mistakes to Avoid
- Stopping at √72 = 2√18.
- Adding what’s inside: √2 + √3 ≠ √5.
- Taking out a factor that doesn’t repeat enough.
Frequently Asked Questions
- How do I simplify √50?
- 5√2.
- When is a radical simplest?
- When no perfect power of its index divides the radicand.
- Can I add √8 and √18?
- Yes: 2√2 + 3√2 = 5√2.