Question

solve for v.
$v^2 = 121$
$v = \boxed{}$ or $\boxed{}$

Explanation:

Step1: Take square root of both sides

To solve for \( v \) when \( v^2 = 121 \), we take the square root of both sides of the equation. The square root of a number \( x^2 \) is \( \pm x \) because both \( x \) and \( -x \) when squared give \( x^2 \). So, taking the square root of both sides, we get:

$$ \sqrt{v^2}=\sqrt{121} $$

Step2: Simplify the square roots

Simplifying the left side, \( \sqrt{v^2} = |v| \), but since we are looking for all real solutions, we can consider the positive and negative roots. The square root of 121 is 11 because \( 11\times11 = 121 \) and \( (-11)\times(-11)=121 \). So, simplifying both sides, we have:

$$ v=\pm11 $$

Answer:

\( v = 11 \) or \( v = -11 \)