CalcWhenSquare Root Calculator
The square root of 144 is exactly 12 — a perfect square, sitting in the friendly sequence 1, 4, 9, 16, 25, 36, 49, 64, 81, 100, 121, 144.
How it works
Type a number and get its square root to six decimals — plus the things homework and real problems ask alongside: the cube root, the number squared, whether it is a perfect square, and the simplified radical (√72 becomes 6√2) that textbooks insist on.
Negative numbers get an honest answer instead of an error beep: no real square root exists, and the panel says why in one line.
The method
Roots are computed in double precision (√n to 6 decimals displayed). Perfect-square detection checks whether the root is whole. Radical simplification finds the largest square factor b² dividing n and rewrites √n as b√(n/b²).
Frequently asked questions
What is the square root of 2?
1.414214 (to six places) — famously irrational, proved by the ancient Greeks, and the diagonal of a unit square. It never terminates and never repeats.
Why does √72 simplify to 6√2?
Because 72 = 36 × 2, and 36 is a perfect square whose root (6) can step outside the radical, leaving √2 behind: 6√2 ≈ 8.485281.
Can a negative number have a square root?
Not among real numbers — squaring anything real gives a non-negative result. Negative roots live in the complex numbers, written with i, which this calculator leaves to algebra class.