√

SquareRoot

Math

The SquareRoot block calculates the n-th root of the input signal. While named SquareRoot for common usage (where n=2), it is a versatile root-calculation block that supports cube roots (n=3) and any other numeric root order.

Mathematical Model

The block implements the following calculation:

y(t) = \sqrt[n]{u(t)}

Where:

y(t) is the output signal
in(t) is the input signal
n is the root order (default is 2.0)

Handling of Negative Inputs

Calculating the root of a negative number can be problematic for even root orders (e.g., √-1). The block provides several configurable safety modes:

Return Zero (Default): Outputs 0.0 when a negative input is encountered. This is the safest option for simulation stability and includes a one-time visual warning.
Use Absolute Value: Calculates the root of the absolute value of the input. Useful when the sign of the signal is irrelevant for the root calculation.
Return NaN: Returns "Not a Number". Note that this value will propagate through your diagram and may cause other blocks to output NaN.

Inputs & Outputs

Direction	ID	Label	Type	Status
→ In	`in`	In	number	Required
← Out	`out`	Out	number	Output

Parameters

Parameters	Label	Type	Default
`rootOrder`	Root Order (n)	number	`2`
`negativeHandling`	Negative Input	select	`zero`
`reportWarning`	Report Warning	boolean	`true`

Usage Examples

Distance Calculation

Calculate the distance from coordinates (x, y):

Sum (x^2 + y^2) → SquareRoot (n=2) → Distance

Flow Measurement

Calculate fluid flow rate from differential pressure (where flow ∝ √ΔP):

PressureDifference → SquareRoot (n=2) → FlowRate

Remarks & Best Practices

Negative inputs: Even root orders (n = 2, 4, 6) produce NaN for negative inputs; use the "Use Absolute Value" mode or the "Return Zero" safety option
Zero input: Returns 0 for any positive root order
Root order < 1: Equivalent to raising the input to a power > 1 (e.g., n = 0.5 squares the signal)
Performance: Very low computational cost; safe for real-time simulation
Numerical stability: Root of very small positive numbers can produce large outputs; consider clamping near-zero inputs

Related Components

Product: For general multiplication and squaring (n=0.5)
Gain: For scaling signals
MathFunction: For other mathematical operations