Square Root Calculator

A square root of a number x is a value y such that y × y = x. For example, the square root of 25 is 5 because 5 × 5 = 25. Every positive number has two square roots: a positive and a negative one (both 5 and -5 squared give 25). By convention, the "square root" refers to the principal (positive) root.

A perfect square is a number whose square root is a whole integer. Examples: 1, 4, 9, 16, 25, 36, 49, 64, 81, 100. Non-perfect squares like 2, 3, 5 have irrational square roots — they cannot be expressed as a fraction and their decimal form never ends or repeats (e.g., √2 = 1.41421356...).

To simplify √72: find the largest perfect square that divides 72. That's 36 (since 36 × 2 = 72). Then: √72 = √(36 × 2) = √36 × √2 = 6√2. The simplified form keeps the perfect square outside the radical and the remaining factor inside. Our calculator does this automatically.

Not in real numbers — the square root of a negative number is imaginary. In complex number math, √(-1) = i (the imaginary unit). So √(-9) = 3i. Imaginary numbers are used in electrical engineering, quantum mechanics, and signal processing. Our calculator works with real numbers only.