Which of the

\[n\] values are solutions to the following equation?
\[n^2 = 2.25\]
Choose all answers that apply:
Choose all answers that apply:
(Choice A)
\[n = 1.1\]
A
\[n = 1.1\]
(Choice B)
\[n = -1.1\]
B
\[n = -1.1\]
(Choice C)
\[n = 1.4\]
C
\[n = 1.4\]
(Choice D)
\[n = -1.4\]
D
\[n = -1.4\]
(Choice E) None of the above
E
None of the above

1 answer

To solve the equation

\[ n^2 = 2.25, \]

we can take the square root of both sides:

\[ n = \pm \sqrt{2.25}. \]

Calculating the square root:

\[ \sqrt{2.25} = 1.5. \]

Thus, the solutions for \(n\) are

\[ n = 1.5 \quad \text{and} \quad n = -1.5. \]

Now, let's check each of the provided choices:

  • Choice A: \(n = 1.1\) → Not a solution, since \(1.1^2 = 1.21\) which is not equal to \(2.25\).
  • Choice B: \(n = -1.1\) → Not a solution, since \((-1.1)^2 = 1.21\) which is not equal to \(2.25\).
  • Choice C: \(n = 1.4\) → Not a solution, since \(1.4^2 = 1.96\) which is not equal to \(2.25\).
  • Choice D: \(n = -1.4\) → Not a solution, since \((-1.4)^2 = 1.96\) which is not equal to \(2.25\).
  • Choice E: None of the above → This is correct because none of the choices provided are equal to the actual solutions \(1.5\) or \(-1.5\).

Therefore, the correct answer is:

Choice E: None of the above.