객관식
Simplify the following.
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9. Roots, Radicals, and Complex Numbers
Introduction to Radical Expressions
객관식
Evaluate the radical.
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No real solution (Imaginary)
검증된 단계별 안내1
Recognize the expression inside the square root: \(\sqrt{\left(-5\right)^2}\). This means you are taking the square root of the square of -5.
Recall the property of exponents: squaring a number, whether positive or negative, results in a non-negative value. So, \(\left(-5\right)^2 = (-5) \times (-5)\).
Calculate the square inside the radical: \((-5) \times (-5) = 25\). So the expression becomes \(\sqrt{25}\).
Understand that the square root function \(\sqrt{x}\) returns the principal (non-negative) square root of \(x\). Therefore, \(\sqrt{25}\) is the non-negative number which, when squared, gives 25.
Conclude that the value of \(\sqrt{\left(-5\right)^2}\) is the positive number 5, because the square root function always returns the principal (non-negative) root.
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