How it works
The nth root of a number is whatever value, multiplied by itself n times, gets back to that number. A "perfect" root — like 64 for a square root — lands exactly on a whole number; most numbers don't, and the calculator flags which case you're in.
n√x = x1/n
Worked example
The square root of 64.
- Find the number that, multiplied by itself, gives 64: 8 × 8 = 64.
√64 = 8, an exact whole number.
Common questions
What does "surd" mean?
A surd is a root that doesn't simplify to a whole number — √2 and √10 are surds, while √4 and √9 are not, since those simplify to 2 and 3.
Can you take the square root of a negative number?
Not as a real number — no real number squared gives a negative result, so this calculator flags it as undefined. Odd roots are different: the cube root of −8 is a perfectly real −2, since (−2)³ = −8.
What counts as an "exact" result?
The calculator checks whether rounding to the nearest whole number and raising it back to the nth power lands exactly back on your original number. If so, it's exact; if the round-trip is off even slightly, it's an approximation.