Multiple Choice
Simplify the root.
9. Roots, Radicals, and Complex Numbers
Introduction to Radical Expressions
Multiple Choice
Simplify the following.
A
B
C
D
Verified step by step guidance1
Identify the expression to simplify: \(^3\sqrt{\left(-5\right)^3}\), which means the cube root of \((-5)^3\).
Recall the property of radicals and exponents: \(^n\sqrt{a^n} = a\) when \(n\) is an odd integer, because the root and the power cancel each other out.
Since the cube root (3rd root) and the cube (power of 3) are inverse operations, simplify inside the radical first: \(\left(-5\right)^3\) remains as is, but the cube root will undo the cube.
Apply the cube root to \((-5)^3\), which simplifies to just \(-5\) because the cube root of a cube returns the base, preserving the sign for odd roots.
Conclude that the simplified form of \(^3\sqrt{\left(-5\right)^3}\) is \(-5\).
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