Question

Solve X^2 = 45 , where x is a real number .

Answer 1

The given equation is

$x^2=45$

To solve it, take a square root for each side

$\begin{gathered} \sqrt[]{x^2}=\pm\sqrt[]{45} \\ x=\pm\sqrt[]{45} \end{gathered}$

Since 45 = 5 x 9, then

$\begin{gathered} x=\pm\sqrt[]{9\times5} \\ x=\pm\sqrt[]{9}\times\sqrt[]{5} \\ x=\pm3\sqrt[]{5} \end{gathered}$

The solutions are

$x=-3\sqrt[]{5},3\sqrt[]{5}$