To solve the expression \( 4 \sqrt{a^2 - b^2} \) with \( a = -5 \) and \( b = 3 \), follow these steps:
1. Substitute the given values of \( a \) and \( b \):
- \( a = -5 \)
- \( b = 3 \)
2. Calculate \( a^2 \):
[tex]\[
a^2 = (-5)^2 = 25
\][/tex]
3. Calculate \( b^2 \):
[tex]\[
b^2 = 3^2 = 9
\][/tex]
4. Subtract \( b^2 \) from \( a^2 \):
[tex]\[
a^2 - b^2 = 25 - 9 = 16
\][/tex]
5. Take the square root of the result:
[tex]\[
\sqrt{a^2 - b^2} = \sqrt{16} = 4
\][/tex]
6. Multiply the result by 4:
[tex]\[
4 \sqrt{a^2 - b^2} = 4 \times 4 = 16
\][/tex]
Therefore, when [tex]\( a = -5 \)[/tex] and [tex]\( b = 3 \)[/tex], the value of the expression is [tex]\( 16.0 \)[/tex].
