Subjects algebra

Root Over Square

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Root Over Square


1. Let's first clarify the problem statement. You have an expression where the square root applies only to the squared part of it, not the entire expression. 2. For example, if the expression is $\sqrt{x^2 + 4}$, the square root applies over $x^2 + 4$. But if the root is only over the squared part, it means $\sqrt{(x^2)} + 4$. 3. We know that $\sqrt{x^2} = |x|$, which means the absolute value of $x$. 4. So the expression becomes $|x| + 4$. 5. This distinction helps in correctly simplifying or evaluating the expression because the root over the square cancels the square but preserves the absolute value. Final answer: When the root is only over the squared part of the expression, it simplifies to the absolute value of the base of the square plus the other terms outside the root, e.g. $\sqrt{x^2} + 4 = |x| + 4$.