Final answer:
To solve the equation x²=12, take the square root of both sides to get x = ±√12, which simplifies to x = ±(2√3). Both positive and negative square roots should be considered, leading to two real number solutions.
Step-by-step explanation:
To solve the equation x²=12 using the square root property, we first take the square root of both sides of the equation. Remember, when you take the square root of a variable squared, you include both the positive and negative solutions. Therefore, the solution to the equation will be:
x = ±√12
Breaking down the steps further:
Take the square root of both sides: √x² = √12
Simplify the square root: x = ±√(4⋅ 3)
Reduce the square root: x = ±(2√3), since 4 is a perfect square and equals 2 when square rooted
The solutions x = 2√3 and x = -2√3 are the real number solutions to the equation.