Question

solve for a. express your answer in simplest radical form if necessary.\\(a^2 = 33\\)\
answer attempt 1 out of 3\
\\(\odot\\) additional solution \\(\ominus\\) no solution\
\\(a = \\)\
submit answer

Explanation:

Step1: Take square root of both sides

To solve for \( a \) in the equation \( a^2 = 33 \), we take the square root of both sides. Remember that when we take the square root of a number, we get both a positive and a negative solution because \( (\pm x)^2 = x^2 \). So, we have \( \sqrt{a^2} = \pm\sqrt{33} \).

Step2: Simplify the left side

The square root of \( a^2 \) is just \( |a| \), but since we're looking for all real solutions, we can write \( a = \pm\sqrt{33} \) because the square root function (when considering real numbers) gives the principal root (positive), and the negative of that is also a solution.

Answer:

\( \pm\sqrt{33} \) (or you can write \( \sqrt{33} \) and \( -\sqrt{33} \) separately, but \( \pm\sqrt{33} \) is the concise form for both solutions)