Calculate & Simplify Square Roots
Find square roots with decimal precision and radical form simplification. Includes perfect square detection, prime factorization, and nearest perfect squares.
How It Works
√n = n^(1/2)The square root of a number n is the value that, when multiplied by itself, equals n. Perfect squares (1, 4, 9, 16, 25...) have integer square roots. Non-perfect squares can be simplified to radical form: √72 = 6√2.
Quick Tips
Perfect Squares
1, 4, 9, 16, 25, 36, 49, 64, 81, 100 — their square roots are 1-10.
Simplification
√72 = √(36×2) = 6√2. Extract the largest perfect square factor.
Mental Math
√50 ≈ 7.07 because 7²=49 and 8²=64. Estimate between perfect squares.
Prime Factorization
72 = 2³×3². Pair up factors: (2×3)√2 = 6√2.
Step-by-Step Instructions
- 1Enter the number you want to find the square root of.
- 2Click Calculate to see the decimal value and simplified radical form.
- 3Check the prime factorization and nearest perfect squares for reference.
Frequently Asked Questions
What is a perfect square?▼
A perfect square is a number that is the square of an integer. Examples: 1 (1²), 4 (2²), 9 (3²), 16 (4²), 25 (5²). Perfect squares have integer square roots.
How do I simplify √72?▼
Find the largest perfect square factor: 72 = 36 × 2. Since √36 = 6, we get √72 = 6√2. Our calculator does this automatically using prime factorization.
Can I find the square root of a negative number?▼
In real numbers, no — negative numbers don't have real square roots. In complex numbers, √(-n) = i√n where i is the imaginary unit. Our calculator works with non-negative numbers.