Question

solve ( x^2 = 45 ), where ( x ) is a real number.
simplify your answer as much as possible.

if there is more than one solution, separate them with commas.
if there is no solution, click
o solution.\

( x = square )

Explanation:

Step1: Take square root of both sides

To solve the equation \( x^2 = 45 \), we take the square root of both sides. Remember that for an equation \( x^2 = a \) (where \( a\geq0 \)), the solutions are \( x = \sqrt{a} \) and \( x = -\sqrt{a} \). So, taking the square root of both sides of \( x^2 = 45 \), we get \( x=\pm\sqrt{45} \).

Step2: Simplify the square root

Simplify \( \sqrt{45} \). We can factor 45 as \( 9\times5 \), and since \( \sqrt{9\times5}=\sqrt{9}\times\sqrt{5} \) (by the property \( \sqrt{ab}=\sqrt{a}\times\sqrt{b} \) for \( a\geq0,b\geq0 \)), and \( \sqrt{9} = 3 \), so \( \sqrt{45}=3\sqrt{5} \). Therefore, the solutions are \( x = 3\sqrt{5}, - 3\sqrt{5} \).

Answer:

\( 3\sqrt{5}, -3\sqrt{5} \)