Simplifying radicals means rewriting √n as a whole number times a smaller root.
About this calculator
Simplifying radicals means rewriting √n as a whole number times a smaller root. √72 = √(36 × 2) = 6√2. The 36 comes out as 6; the 2 stays inside because it has no square factors.
Teachers expect the radicand to be square-free — no 4, 9, 25, etc. left inside. The decimal value is included for checking your work on a calculator.
Works with the [[square-root]] calculator for the full evaluation. For higher roots see [[root]]. For expressions like √(a² − b²) try [[difference-of-two-squares]].
Common uses
- Simplify √72 to 6√2 for homework
- Check whether a radical is fully simplified
- Prepare answers before rationalizing denominators
- Compare decimal and exact radical forms
- Practice factoring perfect squares from radicands
Frequently asked questions
How do you simplify √72?
72 = 36 × 2. √36 = 6, so √72 = 6√2. The 2 stays inside because it is square-free.
What does square-free radicand mean?
No perfect-square factor remains inside. √50 simplifies to 5√2, not √(25 × 2) with 25 still hidden.
Can you simplify √50 further?
√50 = 5√2. Since 2 has no square factors, this is fully simplified.
What is the decimal of 6√2?
6√2 ≈ 6 × 1.414 ≈ 8.485. The simplified form is exact; the decimal is an approximation.