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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].

Sagot :

GinnyAnswer
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].
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