Questions: Quadratic and Polynomial Functions Solving a quadratic equation using the square root property: Exact... Solve x^2=27, 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 "No solution." x=

Quadratic and Polynomial Functions Solving a quadratic equation using the square root property: Exact... Solve x^2=27, 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 "No solution." x=
Transcript text: Quadratic and Polynomial Functions Solving a quadratic equation using the square root property: Exact... Solve $x^{2}=27$, 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 "No solution." \[ x= \] $\square$ $\square$
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Solution

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Solution Steps

Step 1: Apply the square root property

To solve the equation \(x^{2} = 27\), we take the square root of both sides. This gives: \[ x = \pm \sqrt{27} \]

Step 2: Simplify the square root

The square root of 27 can be simplified by factoring out perfect squares: \[ \sqrt{27} = \sqrt{9 \times 3} = \sqrt{9} \times \sqrt{3} = 3\sqrt{3} \]

Step 3: Write the final solutions

Substituting the simplified square root back into the equation, we get: \[ x = \pm 3\sqrt{3} \]

Final Answer

\[ \boxed{x = 3\sqrt{3}, -3\sqrt{3}} \]

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