Explanation
Let's assume we have a squared expression like this one:
[tex]a^2=b[/tex]
We can apply a square root to both sides which will turn the squared a into an absolute value:
[tex]\begin{gathered} \sqrt{a^2}=\sqrt{b} \\ |a|=\sqrt{b} \end{gathered}[/tex]
The module tells us that this equation is turned into two:
[tex]\begin{gathered} a=\sqrt{b} \\ a=-\sqrt{b} \end{gathered}[/tex]
We can use this with the expression given by the question:
[tex]\begin{gathered} t^2=75 \\ \sqrt{t^2}=\sqrt{75} \\ |t|=\sqrt{75} \end{gathered}[/tex]
So we have two values for t:
[tex]\begin{gathered} t=\sqrt{75} \\ t=-\sqrt{75} \end{gathered}[/tex]
We still need to write them in simplest form. For this purpose we'll have to rewrite 75:
[tex]\begin{gathered} \sqrt{75}=\sqrt{3\cdot25}=\sqrt{3}\cdot\sqrt{25} \\ \sqrt{75}=5\sqrt{3} \end{gathered}[/tex]Answer
Therefore the answers are:
[tex]t=-5\sqrt{3},5\sqrt{3}[/tex]
