Consider this expression:

[tex]\[ 4 \sqrt{a^2 - b^2} \][/tex]

Type the correct answer in the box. Use numerals instead of words.

When [tex] a = -5 [/tex] and [tex] b = 3 [/tex], the value of the expression is [tex] \square [/tex].



Answer :

To determine the value of the expression [tex]\( 4 \sqrt{a^2 - b^2} \)[/tex] when [tex]\( a = -5 \)[/tex] and [tex]\( b = 3 \)[/tex], follow these steps:

1. Compute [tex]\( a^2 \)[/tex]:
[tex]\[ a = -5 \implies a^2 = (-5)^2 = 25 \][/tex]

2. Compute [tex]\( b^2 \)[/tex]:
[tex]\[ b = 3 \implies b^2 = 3^2 = 9 \][/tex]

3. Subtract [tex]\( b^2 \)[/tex] from [tex]\( a^2 \)[/tex]:
[tex]\[ a^2 - b^2 = 25 - 9 = 16 \][/tex]

4. Take the square root of the result:
[tex]\[ \sqrt{16} = 4 \][/tex]

5. Multiply by 4:
[tex]\[ 4 \times 4 = 16 \][/tex]

Therefore, the value of the expression [tex]\( 4 \sqrt{a^2 - b^2} \)[/tex] when [tex]\( a = -5 \)[/tex] and [tex]\( b = 3 \)[/tex] is [tex]\( \boxed{16} \)[/tex].