Square Root Calculator
Calculate principal and secondary square roots, and identify perfect squares.
Quick Examples
Principal Square Root
Principal Complex Root
Negative numbers have imaginary roots ($i = \sqrt{-1}$)
Principal (Positive) Root
Secondary (Negative) Root
Explanation
The square roots of are
and .
Because × =
And × () =
The principal root of involves an imaginary number i.
$\sqrt{} = \sqrt{ \times -1}$
$= \sqrt{} \times \sqrt{-1}$
$= $
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About Square Root Calculator
What is a Square Root?
The square root of a number $x$ is a number $y$ such that $y^2 = x$. Every positive real number has two square roots: one positive (called the principal square root) and one negative. For example, the square roots of 25 are 5 and -5.
How to Use This Calculator
- Enter the number you wish to find the square root of.
- The calculator will instantly display the principal (positive) root, the secondary (negative) root, and indicate whether the number is a perfect square.
- If you enter a negative number, the calculator will compute the principal complex root (imaginary numbers).
Perfect Squares
A perfect square is an integer that is the square of an integer. Examples include 1, 4, 9, 16, 25, 36, 49, 64, 81, and 100. Our calculator automatically identifies if your input is a perfect square.
Imaginary Roots
The square root of a negative numbers involves imaginary numbers (represented by $i$, where $i = \sqrt{-1}$). For instance, the principal square root of -16 is $4i$. Our calculator supports negative inputs and will provide the complex root result.
Features
- Real-time calculation.
- Identifies perfect squares.
- Calculates positive and negative roots.
- Computes imaginary roots for negative inputs.
Frequently Asked Questions
What is a principal square root?
The principal square root referes to the non-negative (positive) square root of a non-negative real number.
Can I find the square root of a negative number?
Yes! The result belongs to the set of complex (imaginary) numbers. The square root of a negative number $-x$ is $i\sqrt{x}$.