Evaluate the following square root. − 121 -\sqrt{121}

we're asked to evaluate the following square root, negative square root of 121. Now the first thing I notice here is this negative. Since this negative is outside of that radical, that is okay. If it was inside my radical, then it would be imaginary, and I would have no real solution. But since it's on the outside, we can proceed as normal here. We're looking for a value that when squared gives us 121. Thinking about this, the first thing I think is I know that 10 squared is 100. That's an easy one. So this should be a value that's greater than 10. So let's start with 11. 11 squared will give me 121. So that's exactly what I'm looking for. But 11 is not my solution here because remember, we're looking for negative square root of 121. So while 11 squared does give me what's underneath my radical, I then need to put a negative on the outside because that's what was asked of me here. So my solution here is negative 11. Let me know if you have questions in the comments, and I'll see you in the next one.

9. Roots, Radicals, and Complex Numbers

Introduction to Radical Expressions

Intermediate Algebra

9. Roots, Radicals, and Complex Numbers

Introduction to Radical Expressions

Struggling with Intermediate Algebra?

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Multiple Choice

Evaluate the following square root.
$- \sqrt{121}$

$11i$

$11$

$-11$

$-10$

Verified step by step guidance

Identify the expression to evaluate: the negative square root of 121, written as $-\sqrt{121}$.

Recall that the square root symbol $\sqrt{\cdot}$ represents the principal (non-negative) square root of a number.

Calculate the square root of 121 by finding the number which, when squared, equals 121. This means solving $x^2 = 121$ for $x$.

Since 121 is a perfect square, determine its positive square root value.

Apply the negative sign in front of the square root to get the final expression: $-\sqrt{121}$ equals the negative of the positive root found in the previous step.

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Evaluate the following square root.−121-\sqrt{121}

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Evaluate the following square root.
$- \sqrt{121}$