Multiple Choice
Determine if the given square root evaluates to a real number.
9. Roots, Radicals, and Complex Numbers
Introduction to Radical Expressions
Multiple Choice
Simplify the root.
A
B
C
D
Verified step by step guidance1
Identify the expression to simplify: \(-^4\\sqrt{10,000}\), which means the negative of the fourth root of 10,000.
Rewrite 10,000 as a power of 10 to make it easier to work with roots. Since \$10,000 = 10^4$, substitute this into the expression.
Apply the property of radicals that \(\\sqrt[n]{a^m} = a^{\\frac{m}{n}}\). Here, the fourth root of \$10^4$ is \(10^{\\frac{4}{4}}\).
Simplify the exponent: \(10^{\\frac{4}{4}} = 10^1 = 10\).
Don't forget the negative sign outside the root, so the simplified expression is \(-10\).
Related Videos
Related Practice