Simplify Radicals Calculator
Simplify square roots, cube roots and fourth roots to simplest radical form, like √72 = 6√2.
About the Simplify Radicals Calculator
Choose square, cube or fourth root, enter the whole number under the root and any coefficient in front. The calculator gives the simplest radical form, the decimal value and the prime-factor working.
A radical is in simplest form when no factor under the root sign is a perfect square (or cube, for cube roots). Factor the number into primes, take each prime out once for every complete pair (or triple), and leave the rest inside.
The formula
√(a² × b) = a√b
Worked example
Simplify √72
- 72 = 2³ × 3² = (2 × 3)² × 2
- √72 = 6√2 ≈ 8.485
Questions people ask
Is √50 = 5√2?
Yes, because 50 = 25 × 2.
What about a fraction under the root?
Simplify the top and bottom separately, then rationalise the denominator.