Evaluate the radical. ( − 5 ) 2 \sqrt{\left(-5\right)^2} ( − 5 ) 2 <path d="M983 90l0 -0c4,-6.7,10,-10,18,-10 H400000v40H1013.1s-83.4,268,-264.1,840c-180.7,572,-277,876.3,-289,913c-4.7,4.7,-12.7,7,-24,7s-12,0,-12,0c-1.3,-3.3,-3.7,-11.7,-7,-25c-35.3,-125.3,-106.7,-373.3,-214,-744c-10,12,-21,25,-33,39s-32,39,-32,39c-6,-5.3,-15,-14,-27,-26s25,-30,25,-30c26.7,-32.7,52,-63,76,-91s52,-60,52,-60s208,722,208,722c56,-175.3,126.3,-397.3,211,-666c84.7,-268.7,153.8,-488.2,207.5,-658.5c53.7,-170.3,84.5,-266.8,92.5,-289.5zM1001 80h400000v40h-400000z">

Everyone. Let's take a look at our practice problem here. We've got the square root of negative 5 squared. Now, one of the things you might be thinking of is, well, Patrick, I thought you told me that I can't have negatives inside of square roots, and I did. That's perfectly true. You can have negatives in square roots, but this one's different because I don't just have negative 5 by itself. I have negative 5 that's raised to a power. It's raised to the second power over here. So one of the things I can do in this radical is I can actually just evaluate what's inside the radical first. This just becomes the square root of what's negative twenty what's negative 5 times itself? It actually just becomes positive 25. So this thing doesn't lead to an imaginary root because it's not just negative 5 by itself, It's negative 5 squared. So you can evaluate that first, turn it to 25. And now what is this asking you? It's asking you for what is the roots of 25, and that's positive, and this actually just turns out to be positive 5. So that is the answer. Alright? So a little bit of a strange question, but you might see this, but, you know, you might see this in your homeworks and your quizzes and stuff, so it's good to know. Thanks for watching.

0. Review of Algebra

Radical Expressions

College Algebra

0. Review of Algebra

Radical Expressions

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Multiple Choice

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

$2.23$

$5$

$-5$

No real solution (Imaginary)

Verified step by step guidance

Start by evaluating the expression inside the radical: $(-5)^2$. This means you need to square -5.

Calculate $(-5)^2$. Remember that squaring a negative number results in a positive number, so $(-5)^2 = 25$.

Now, substitute the result back into the radical expression: $\sqrt{25}$.

Evaluate $\sqrt{25}$. The square root of 25 is 5, since 5 multiplied by itself equals 25.

Consider the context of the problem. If the problem specifies a negative result or imaginary solution, check if there are additional conditions or interpretations needed.