How to Use Square Root & Cube Root Calculator
- Enter Number: Input the radicand value.
- Select Root: Choose square root (√), cube root (∛), or custom N-th root.
- Click Calculate: View the exact decimal answer and simplified radical form.
Explanation & How It Works
The square root of a number $x$ is a value $y$ such that $y^2 = x$. Perfect squares (such as 1, 4, 9, 16, 25, 36, 49, 64, 81, 100) yield whole integer roots, while non-perfect squares produce irrational numbers with infinite decimals.
Calculation Formula & Rules
√x = x^(1/2) | ∛x = x^(1/3) | ⁿ√x = x^(1/n)
Example Calculation
Example: Calculate √144 and √50.
- √144 = 12 (since 12 × 12 = 144, a perfect square).
- √50 = √(25 × 2) = 5√2 ≈ 7.0710678.
Table of First 20 Perfect Squares
1, 4, 9, 16, 25, 36, 49, 64, 81, 100, 121, 144, 169, 196, 225, 256, 289, 324, 361, 400.
Frequently Asked Questions
Can you take the square root of a negative number?
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In real numbers, no. In complex mathematics, the square root of -1 is defined as the imaginary unit i (√-1 = i).