Question

solve $t^2 = 289$. simplify your answer as much as possible. if there is more than one solution, separate them with commas. $t = \square$

Explanation:

Step1: Take square root of both sides

To solve the equation \( t^2 = 289 \), 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 \( (\pm a)^2=a^2 \). So we have \( t=\pm\sqrt{289} \).

Step2: Simplify the square root

We know that \( 17\times17 = 289 \) and \( (- 17)\times(-17)=289 \), so \( \sqrt{289} = 17 \) and \( -\sqrt{289}=- 17 \).

Answer:

\( t = 17, - 17 \)