Question

simplify
-square root of 9y^2 if y<0

Answer 1

To simplify \(-\sqrt{9y^2}\) given that \(y < 0\), we can follow these steps:

1. Start with the expression:
\[
-\sqrt{9y^2}
\]

2. Factor out the constants:
\[
-\sqrt{9} \cdot \sqrt{y^2}
\]

3. Since \(\sqrt{9} = 3\), we have:
\[
-3\sqrt{y^2}
\]

4. The square root of \(y^2\) is \(|y|\). However, because we know \(y < 0\), \(|y| = -y\). Therefore:
\[
\sqrt{y^2} = -y
\]

5. Substitute this back into the expression:
\[
-3(-y) = 3y
\]

So, the simplified expression for \(-\sqrt{9y^2}\) when \(y < 0\) is:
\[
3y
\]