sqrt9x2

sqrt9x2 refers to the mathematical expression "the square root of 9 times x squared". This expression can be simplified using the properties of square roots. The square root of a product is equal to the product of the square roots, meaning $\sqrt{ab} = \sqrt{a} \times \sqrt{b}$. Therefore, $\sqrt{9x^2}$ can be rewritten as $\sqrt{9} \times \sqrt{x^2}$. The square root of 9 is 3, and the square root of $x^2$ is $|x|$, the absolute value of x. This is because squaring a negative number results in a positive number, so the square root of $x^2$ must be non-negative. Thus, the simplified form of $\sqrt{9x^2}$ is $3|x|$. Without the absolute value, the expression would only be valid for non-negative values of x. In algebra, when dealing with variables under square roots that can be negative, it is crucial to consider the absolute value to ensure the result is always correct. Therefore, $\sqrt{9x^2}$ is equivalent to $3|x|$.