Question
simplify
- sqaure root of 16y^2 if y<0
- sqaure root of 16y^2 if y<0
Answers
GPT-4o mini
To simplify \(- \sqrt{16y^2}\), we can start by breaking it down:
1. First, find the square root:
\[
\sqrt{16y^2} = \sqrt{16} \cdot \sqrt{y^2} = 4|y|
\]
2. Since \(y < 0\), we have \(|y| = -y\).
3. Substitute \(-y\) for \(|y|\):
\[
\sqrt{16y^2} = 4(-y) = -4y
\]
4. Now, applying the negative sign from the original expression:
\[
-\sqrt{16y^2} = -(-4y) = 4y
\]
So, the simplified expression is:
\[
4y
\]
1. First, find the square root:
\[
\sqrt{16y^2} = \sqrt{16} \cdot \sqrt{y^2} = 4|y|
\]
2. Since \(y < 0\), we have \(|y| = -y\).
3. Substitute \(-y\) for \(|y|\):
\[
\sqrt{16y^2} = 4(-y) = -4y
\]
4. Now, applying the negative sign from the original expression:
\[
-\sqrt{16y^2} = -(-4y) = 4y
\]
So, the simplified expression is:
\[
4y
\]