Which of the

\[a\] values are solutions to the following equation?
\[a^2 = 6.4\]
Choose all answers that apply:
Choose all answers that apply:
(Choice A)
\[a = -0.8\]
A
\[a = -0.8\]
(Choice B)
\[a = 0.8\]
B
\[a = 0.8\]
(Choice C)
\[a = -3.2\]
C
\[a = -3.2\]
(Choice D)
\[a = 3.2\]
D
\[a = 3.2\]
(Choice E) None of the above
E
None of the above

1 answer

To solve the equation \(a^2 = 6.4\), we first take the square root of both sides. This gives us two possible values for \(a\):

\[a = \sqrt{6.4} \quad \text{or} \quad a = -\sqrt{6.4}\]

Now, let's calculate \(\sqrt{6.4}\):

\[ \sqrt{6.4} \approx 2.529822 (to, 6, decimal, places) \]

Thus, the two potential solutions for \(a\) are approximately:

\[ a \approx 2.529822 \quad \text{or} \quad a \approx -2.529822 \]

Now, let's evaluate the options given:

  • Choice A: \(a = -0.8\) (not a solution)
  • Choice B: \(a = 0.8\) (not a solution)
  • Choice C: \(a = -3.2\) (not a solution)
  • Choice D: \(a = 3.2\) (not a solution)
  • Choice E: None of the above (this is the correct answer)

Since none of the choices provided match our calculated solutions, the correct selection is:

\[ \text{(Choice E) None of the above} \]