Multiple Choice
Simplify the following.
11. 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 involves the 8th root of \( (x+1)^8 \), written as \( \sqrt[8]{(x+1)^8} \).
Recall the property of radicals and exponents: \( \sqrt[n]{a^n} = |a| \) when \(n\) is even, because even roots return the principal (non-negative) root.
Apply this property to simplify \( \sqrt[8]{(x+1)^8} \) to \( |x+1| \), the absolute value of \( x+1 \).
Include the negative sign outside the radical, so the entire expression becomes \( -|x+1| \).
Thus, the simplified form of the original expression is \( -|x+1| \).
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