Multiple Choice
Use a calculator to evaluate the following and round to the nearest hundredths.
9. Roots, Radicals, and Complex Numbers
Introduction to Radical Expressions
Multiple Choice
Simplify the following.
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Verified step by step guidance1
Recognize that the expression is a fourth root of a quantity raised to the fourth power: \(^4\sqrt{(2 - a)^4}\).
Recall the property of radicals and exponents: \(^n\sqrt{x^n} = |x|\) when \(n\) is even, because the root of an even power returns the absolute value of the base.
Apply this property to simplify \(^4\sqrt{(2 - a)^4}\) to \(|2 - a|\).
Understand that the absolute value ensures the result is non-negative regardless of whether \$2 - a$ is positive or negative.
Conclude that the simplified form of the original expression is \(|2 - a|\).
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