To determine the value of [tex]\( a \)[/tex], given the equation [tex]\( a^2 - 64 = 0 \)[/tex] and the condition [tex]\( a > 0 \)[/tex], follow these steps:
1. Start with the given equation:
[tex]\[
a^2 - 64 = 0
\][/tex]
2. Isolate the squared term:
[tex]\[
a^2 = 64
\][/tex]
3. Take the square root of both sides to solve for [tex]\( a \)[/tex]:
[tex]\[
a = \pm \sqrt{64}
\][/tex]
4. Calculate the square root of 64:
[tex]\[
a = \pm 8
\][/tex]
5. Apply the given condition [tex]\( a > 0 \)[/tex]:
Since [tex]\( a \)[/tex] must be positive,
[tex]\[
a = 8
\][/tex]
Therefore, the value of [tex]\( a \)[/tex] is [tex]\( 8 \)[/tex].
The correct answer is:
C 8
