justyourcalculatorRoot Calculator
Square, cube or any root, as a decimal and in simplest radical form.
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Root Calculator
Square, cube and nth roots, simplified
√72
8.485281374239
Exact: 6√2
- Simplified radical form
- 6√2
How it was calculated
- √x = x^(1/2)
- 72 = 2³ × 3²
- Take out each group of 2 equal primes: 2³ puts 2 outside, 3² puts 3 outside
- √72 = 6√2
- Check: 8.485281374239^2 ≈ 72
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How the root calculator works
The nth root of x is the number that, multiplied by itself n times, gives x: ⁿ√x = x^(1/n). The square root (n = 2) of 49 is 7, and the cube root (n = 3) of 27 is 3.
For whole numbers, the root is also simplified: factor the number into primes, pull out each prime that appears n times, and leave the rest under the root. √72 = √(2³ × 3²) = 6√2.
Even roots of negative numbers aren't real (√-16 = 4i), while odd roots of negative numbers are negative (∛-8 = -2).
Using and checking your result
Published by JustYourCalculator. Check the units and assumptions above, and compare a known example before relying on the output. Calculations use browser arithmetic and may round displayed values.
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