Need to calculate nth roots? Root Calculator answers in seconds. Type Number and Root into Root; each keystroke re-runs the math. Root ties each output to its formula. Root works for one check or many. No account is needed for Root. The browser does the arithmetic. Root handles free root calculator the same way as free online root calculator — one of the Math tools on CalcProMaster. Root is designed for real people. Labels stay plain. Start with Root; the first number takes seconds.
What the defaults give
The cube root of 64 is 4.0000.
Multiplying 4 by itself three times returns 64, which is what the third root asks for.
The rule
ⁿ√x = x^(1/n)
64^(1/3) = 64^0.3333 = 4. The root is the inverse of a power: if 4³ = 64, then the third root of 64 is 4.
Worked examples
²√81 = 9 (9 × 9 = 81)
³√27 = 3 (3 × 3 × 3 = 27)
³√64 = 4
⁴√16 = 2 (2 × 2 × 2 × 2 = 16)
³√−8 = −2 (−2 × −2 × −2 = −8)
²√2 = 1.4142 (irrational, so the decimal never ends)
Even roots and negative numbers
An even root of a negative number has no real answer: no real number squared gives −9, because squaring always produces a non-negative result. An odd root does work, because an odd count of negative factors stays negative — which is why the cube root of −8 is −2 while the square root of −9 is not a real number. That distinction is the most common source of errors when roots are computed by rule rather than checked.
Reading the answer
- Exact versus rounded. Perfect powers give clean results; everything else is rounded, so ²√2 shown to four places is not the exact value.
- Fractional roots. A root of 0.5 is the same as a square root, and 1.5 is the cube root squared — the exponent form handles both.
- Roots of decimals. The square root of 0.25 is 0.5, smaller than the input, which surprises people used to roots growing numbers.
- Order of operations. A root applies to the whole expression under it, so ²√(9 + 16) is 5, while ²√9 + 16 would be 19.
- Precision. Very large or very small inputs lose digits in floating point, so verify a critical result by raising it back to the original power.
Frequently Asked Questions
What is the cube root of 64?
4, because 4 × 4 × 4 = 64. The cube root asks which number multiplied by itself three times gives the input.
Can you take the square root of a negative number?
Not a real one. Even roots of negatives have no real solution; odd roots such as the cube root do, so the cube root of −8 is −2.
How do I calculate a root by hand?
Rewrite it as a fractional exponent: the nth root of x is x to the power 1/n, which a scientific calculator evaluates directly.
Why is the square root of 2 irrational?
Because no fraction of whole numbers squares to exactly 2. The decimal 1.4142 is a rounded approximation, not the value.
What does a root of 0.5 mean?
It is the same as a square root, since 1 divided by 0.5 is 2. Any fractional root is just a different exponent.
Is the square root of 0.25 less than 0.25?
No, it is 0.5, which is larger. Roots of numbers between 0 and 1 grow toward 1 rather than shrinking.
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