Multiple Choice
Evaluate the following square root.
11. Roots, Radicals, and Complex Numbers
Introduction to Radical Expressions
Multiple Choice
Determine if the given square root evaluates to a real number.
A
Real
B
Not Real
C
Cannot be determined
Verified step by step guidance1
Identify the expression given: \(-\sqrt{-25}\), which means the negative of the square root of negative 25.
Recall that the square root of a negative number is not a real number because real numbers squared always give a non-negative result.
Understand that \(\sqrt{-25}\) can be rewritten using imaginary numbers as \(\sqrt{-1 \times 25} = \sqrt{-1} \times \sqrt{25}\).
Since \(\sqrt{-1}\) is defined as the imaginary unit \(i\), rewrite the expression as \(- (i \times 5)\) or \(-5i\).
Conclude that because the expression involves the imaginary unit \(i\), it does not evaluate to a real number.
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