Enter a value n
How it works
- Check that n is a non negative integer.
- Compute k = ⌊√n⌋.
- If k² = n then the index is k.
- Otherwise report √n and the nearest squares k² and (k+1)².
Examples
| n | Is perfect square? | Index k | √n |
|---|---|---|---|
| 0 | Yes | 0 | 0.000000 |
| 1 | Yes | 1 | 1.000000 |
| 4 | Yes | 2 | 2.000000 |
| 7 | No | — | 2.645751 |
| 9 | Yes | 3 | 3.000000 |
| 15 | No | — | 3.872983 |
| 16 | Yes | 4 | 4.000000 |
| 25 | Yes | 5 | 5.000000 |
| 26 | No | — | 5.099020 |
| 144 | Yes | 12 | 12.000000 |
| 200 | No | — | 14.142136 |
Formula
Square sequence: 0², 1², 2², …
Given n, the index is k such that k² = n.
Thus k = √n and k must be an integer for n to lie in the sequence.
FAQs
It is the sequence of perfect squares: 0, 1, 4, 9, 16, 25, … formed by k² for k = 0, 1, 2, …
Compute √n. If it is an integer k, then k is the index because k² = n.
The calculator shows √n and the nearest squares k² and (k+1)² so you can see where n falls between indices.
Yes. The sequence is defined on non negative integers. Decimals will be rejected.
It relies on native integer math and floating point √n. Values up to typical 64 bit integer ranges work well for index checks.
The extra precision helps confirm whether √n is an integer and shows exactly how close n is to a nearby square.
Yes. For n = 0 the index is k = 0 since 0² = 0 is the first square in the sequence.