Multiple Choice
Estimate the square root between two consecutive whole numbers.
9. Roots, Radicals, and Complex Numbers
Introduction to Radical Expressions
Multiple Choice
Simplify the following.
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Verified step by step guidance1
Start by examining the expression: \(^4\sqrt{\left(-x\right)^4}\). This means the fourth root of \((-x)^4\).
Recall that the fourth root and the fourth power are inverse operations, so \(^4\sqrt{a^4} = |a|\) for any real number \(a\). This is because even roots return the principal (non-negative) root.
Apply this property to the expression: \(^4\sqrt{\left(-x\right)^4} = \left| -x \right|\).
Use the property of absolute values that \(\left| -x \right| = |x|\), since absolute value measures distance from zero regardless of sign.
Therefore, the simplified form of the expression is \(|x|\).
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