Question

solve for y.
64 = y²
y = \boxed{} or \boxed{}

Explanation:

Step1: Take square root of both sides

To solve for \( y \) in the equation \( 64 = y^2 \), we take the square root of both sides. Remember that when we take the square root of a number, we consider both the positive and negative roots because \( (\pm a)^2 = a^2 \). So, we have \( \sqrt{64} = \sqrt{y^2} \).

Step2: Simplify the square roots

Simplifying \( \sqrt{64} \), we know that \( 8 \times 8 = 64 \) and \( (-8) \times (-8) = 64 \), so \( \sqrt{64} = \pm 8 \). And \( \sqrt{y^2} = |y| \), but since we are solving for \( y \) and we know that if \( y^2 = 64 \), then \( y \) can be either positive or negative 8 (because both \( 8^2 \) and \( (-8)^2 \) equal 64), we get \( y = \pm 8 \).

Answer:

\( 8 \) or \( -8 \)