Square Root Calculator
The square root of 2 is about 1.414214. The square root of 144 is 12.
- Cube root
- Root of index n
- Simplified radical
- Perfect square
How to use
- Enter a number.
- Read its square root, cube root and perfect-square check straight away.
- For another root, set the index n. For a whole number, the simplified radical form is shown too.
How it works
The square root of x is the number that multiplies by itself to give x. The nth root is the number that gives x when raised to the power n.
To simplify √n, pull out every squared prime factor: 72 = 36 × 2, so √72 = 6√2.
Even roots of negative numbers have no real answer. Odd roots do: the cube root of -8 is -2.
FAQ
What is a perfect square?
A whole number whose square root is also a whole number, such as 1, 4, 9, 16 or 144.
Why does the calculator say there is no real root?
Multiplying a real number by itself never gives a negative result, so √-4 is not a real number. Cube roots and other odd roots accept negative numbers.
What is the simplest radical form used for?
It keeps an exact answer. √72 ≈ 8.485 is rounded, while 6√2 is exact, which matters in algebra and geometry.