Given a right angled triangle with hypotenuse 0f 8 units and one of the other legs as 4 units, we shall calculate the missing side as follows;
[tex]\begin{gathered} The\text{ Pythagoras' theorem states;} \\ c^2=a^2+b^2 \\ \text{Where c is the hypotenuse } \\ a\text{ and b are the other two legs (sides), we now have;} \\ 8^2=AC^2+4^2 \\ 64=AC^2+16 \\ \text{Subtract 16 from both sides;} \\ 64-16=AC^2+16-16 \\ 48=AC^2 \\ \text{Add the square root sign to both sides,} \\ \sqrt[]{48}=\sqrt[]{AC^2} \\ \sqrt[]{48}=AC \\ \end{gathered}[/tex]
The square root of 48 can be simplified further as follows;
[tex]\begin{gathered} \sqrt[]{16}\times\sqrt[]{3}=AC \\ 4\times\sqrt[]{3}=AC \\ \text{Therefore,} \\ AC=4\sqrt[]{3} \end{gathered}[/tex]
ANSWER:
The length of side AC in simplest radical form is,
[tex]AC=4\sqrt[]{3}[/tex]
