Square Root · Power · Log Calculator
Roots, exponents and logarithms in one place
Square Root · nth Root
Exponent (Power)
Logarithm
Squares & Square Roots (1–30)
| n | n² | √n |
|---|---|---|
| 1 | 1 | 1.0000 |
| 2 | 4 | 1.4142 |
| 3 | 9 | 1.7321 |
| 4 | 16 | 2.0000 |
| 5 | 25 | 2.2361 |
| 6 | 36 | 2.4495 |
| 7 | 49 | 2.6458 |
| 8 | 64 | 2.8284 |
| 9 | 81 | 3.0000 |
| 10 | 100 | 3.1623 |
| 11 | 121 | 3.3166 |
| 12 | 144 | 3.4641 |
| 13 | 169 | 3.6056 |
| 14 | 196 | 3.7417 |
| 15 | 225 | 3.8730 |
| 16 | 256 | 4.0000 |
| 17 | 289 | 4.1231 |
| 18 | 324 | 4.2426 |
| 19 | 361 | 4.3589 |
| 20 | 400 | 4.4721 |
| 21 | 441 | 4.5826 |
| 22 | 484 | 4.6904 |
| 23 | 529 | 4.7958 |
| 24 | 576 | 4.8990 |
| 25 | 625 | 5.0000 |
| 26 | 676 | 5.0990 |
| 27 | 729 | 5.1962 |
| 28 | 784 | 5.2915 |
| 29 | 841 | 5.3852 |
| 30 | 900 | 5.4772 |
Log Rules
| Rule | Identity |
|---|---|
| Product → sum | log(xy) = log x + log y |
| Quotient → difference | log(x/y) = log x − log y |
| Power | log(xⁿ) = n·log x |
| Change of base | log_b(x) = ln x ÷ ln b |
| Identities | log_b(b) = 1, log_b(1) = 0 |
FAQ
How do I calculate a square root?
√x is the number that squares to x. Non-perfect squares give irrational results shown as decimals: √2 ≈ 1.4142. Change the degree above for cube and nth roots.
Do negative numbers have square roots?
Not in the real numbers (with imaginary i, √−9 = 3i). Odd-degree roots do work for negatives: ∛−8 = −2.
What is a logarithm?
The exponent needed to reach a number: log₁₀1000 = 3 because 10³ = 1000. Base 10 is the common log; base e (≈2.718) is the natural log (ln).
How do I compute a log in any base?
Use change of base: log_b(x) = ln x ÷ ln b. Pick a custom base above and the calculator applies it.
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