Algebraic Constraint Math Example 3

Follow the full solution, then compare it with the other examples linked below.

Example 3

easy
What constraint does x\sqrt{x} impose on xx?

Solution

  1. 1
    x≥0x \geq 0 (can't take the square root of a negative in the reals).
  2. 2
    The domain of x\sqrt{x} is [0,∞)[0, \infty).

Answer

x≥0x \geq 0
Square roots of negative numbers aren't real, so x\sqrt{x} implicitly constrains xx to be non-negative. This is a domain constraint that must be considered in any problem involving radicals.

About Algebraic Constraint

A mathematical condition expressed as an equation or inequality that restricts which values the variables are allowed to take.

Learn more about Algebraic Constraint →

More Algebraic Constraint Examples

Example 1 easy

What constraint does [formula] impose on [formula]?

Example 2 medium

What values does [formula] constrain [formula] to avoid?

Example 4 medium

If [formula] and [formula], what is the maximum of [formula]?

← All Algebraic Constraint Examples Algebraic Constraint Concept