Multiple Choice
Determine if the given square root evaluates to a real number.
11. Roots, Radicals, and Complex Numbers
Introduction to Radical Expressions
Multiple Choice
Simplify the root.
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Verified step by step guidance1
Identify the expression to simplify: the negative fourth root of 10,000, which can be written as \(-\sqrt[4]{10,000}\).
Rewrite 10,000 as a power of 10: since \$10,000 = 10^4$, substitute this into the expression to get \(-\sqrt[4]{10^4}\).
Apply the property of radicals that \(\sqrt[n]{a^n} = a\) for \(a \geq 0\), so \(\sqrt[4]{10^4} = 10\).
Include the negative sign outside the root, so the expression becomes \(-10\).
Thus, the simplified form of the expression is \(-10\).
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