Question

$\sqrt{a^2}$

Explanation:

Step1: Recall the definition of square root

The square root of a number \( x \), denoted as \( \sqrt{x} \), is a value \( y \) such that \( y^2 = x \). For \( \sqrt{a^2} \), we need to consider the property of square roots and squares.

Step2: Analyze the expression

By the property of square roots, \( \sqrt{x^2}=\vert x\vert \) (the absolute value of \( x \)). So applying this property to \( \sqrt{a^2} \), we get \( \sqrt{a^2}=\vert a\vert \). This is because when we square a number (positive or negative) and then take the square root, we get the non - negative version of that number, which is what the absolute value represents. For example, if \( a = 3 \), then \( \sqrt{3^2}=\sqrt{9} = 3=\vert3\vert \); if \( a=- 3 \), then \( \sqrt{(-3)^2}=\sqrt{9}=3=\vert - 3\vert \).

Answer:

\(\vert a\vert\)