Square root

Summary

• A square root of a real number $a$ is a solution to the equation

$$x^2=a$$

• $2$ and $-2$ are square roots of $4$ (as $2^2={\left( -2 \right)}^2=4$ )
• For $a≥0$ , the equation $x^2=a$ has a unique real non-negative solution
• For $a<0$ , the equation $x^2=a$ has no real solution
• For $a≥0$ , the unique real non-negative solution to the equation is called the principal square root of $a$ .
• The principal square root of $a$ is denoted by $\sqrt{a}$ or $\sqrt[2]{a}$ or $a^{1/2}$ or. Thus, $\sqrt{4}=2$ , not $±2$ .