Question

solve for a.
$a^2 = 144$
$a = \boxed{}$ or $\boxed{}$

Explanation:

Step1: Take square root of both sides

To solve for \( a \) when \( a^2 = 144 \), we take the square root of both sides. The square root of a number \( x^2 \) is \( \pm x \) because both \( x \) and \( -x \) squared give \( x^2 \). So, \( \sqrt{a^2}=\pm\sqrt{144} \).

Step2: Simplify the square roots

We know that \( \sqrt{a^2}=|a| \), but since we are solving for \( a \) in a simple quadratic equation, we can directly find that \( \sqrt{144} = 12 \) (because \( 12\times12 = 144 \)) and \( \sqrt{144}=- 12 \) (because \( (-12)\times(-12)=144 \)). So, \( a=\pm12 \).

Answer:

\( 12 \) or \( -12 \)