Evaluate the radical.
$\sqrt{{(-5)}^2}$

• A. $2.23$
• B. $5$
• C. $-5$
• D. No real solution (Imaginary)

Answer: (B)

Verified step by step guidance

1. 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.
2. Recall the property of exponents: squaring a number, whether positive or negative, results in a non-negative value. So, \(\left(-5\right)^2 = (-5) \times (-5)\).
3. Calculate the square inside the radical: \((-5) \times (-5) = 25\). So the expression simplifies to \(\sqrt{25}\).
4. Understand that the square root of a number is the value that, when squared, gives the original number. Since \(\sqrt{25}\) asks for the non-negative root, it is the positive number whose square is 25.
5. Therefore, the simplified form of \(\sqrt{\left(-5\right)^2}\) is the positive value 5, because the principal square root always returns the non-negative root.