Square Root Calculator
Calculate square roots, cube roots, and any nth root. Simplifies radicals and shows exact results for perfect squares.
√x = x^(1/2). Common perfect squares: √1=1, √4=2, √9=3, √16=4, √25=5, √49=7, √64=8, √81=9, √100=10. To simplify: √48 = √(16×3) = 4√3 ≈ 6.928.
Perfect squares
Square Root Notation by Country
| Country / System | Notation | Calculator key | Curriculum note |
|---|---|---|---|
| 🇺🇸 USA (Common Core) | √x, x^(1/2) | √ key or x^(1/2) | Simplifying radicals is key skill |
| 🇬🇧 UK (GCSE) | √x | √ on Casio fx | Surd form expected in answers |
| 🇩🇪 Germany | Quadratwurzel (√x) | √ on Casio | Irrationale Zahlen (irrational numbers) |
| 🇯🇵 Japan (中学) | √x (ルート x) | √ on CASIO | 根号 — exact form preferred |
| 🇮🇳 India (CBSE) | √x | √ key | Surds chapter in Class 9 |
| 🇨🇳 China | √x (根号) | √ key | 平方根 (square root), 立方根 (cube root) |
| 🇫🇷 France | Racine carrée (√x) | √ on calculatrice | Simplification required |
Frequently Asked Questions
What is the square root of 2?
√2 ≈ 1.41421356237... It is irrational — its decimal expansion never ends or repeats. It appears in the diagonal of a unit square (by the Pythagorean theorem: √(1²+1²) = √2).
How do you simplify √48?
√48 = √(16 × 3) = √16 × √3 = 4√3 ≈ 6.928. The key is finding the largest perfect square factor (16). UK GCSE calls this "surd form."
Can you take the square root of a negative number?
Not in real numbers. √(−1) = i (the imaginary unit). Even roots of negative numbers require complex numbers. Odd roots (∛(−8) = −2) are real.
What is the difference between √9 and ±√9?
The principal square root (√9) is always the positive value: √9 = 3. The ± symbol (±√9 = ±3) appears when solving x² = 9, acknowledging both 3² = 9 and (−3)² = 9. Calculators return the principal root.