Question
Use the square root property to solve the equation. \( t^{2}=27 \)
Ask by Harris Ball. in the United States
Mar 01,2025
Upstudy AI Solution
Tutor-Verified Answer
Answer
The solutions are \( t = 3\sqrt{3} \) and \( t = -3\sqrt{3} \).
Solution
To solve the equation t² = 27 using the square root property, follow these steps:
1. Start with the equation:
t² = 27
2. Apply the square root property, which tells us that if t² = 27, then:
t = ±√27
3. Simplify √27 by factoring under the square root:
√27 = √(9 × 3) = √9 × √3 = 3√3
4. Thus, the solutions are:
t = 3√3 or t = -3√3
So, t = ±3√3 is the solution set.
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Simplify this solution Beyond the Answer
To solve the equation \( t^{2} = 27 \) using the square root property, we take the square root of both sides. This gives us: \[ t = \pm \sqrt{27} \] Since \( \sqrt{27} \) can be simplified to \( 3\sqrt{3} \), the complete solution is: \[ t = 3\sqrt{3} \text{ or } t = -3\sqrt{3} \] So, the two solutions for the equation \( t^{2} = 27 \) are \( t = 3\sqrt{3} \) and \( t = -3\sqrt{3} \). And there you have it—two values of \( t \) waiting to be plugged into your math adventures!
