Question
Use the square root property to solve the equation. \( \mathrm{m}^{2}=17 \)
Ask by Santiago Montgomery. in the United States
Mar 01,2025
Upstudy AI Solution
Tutor-Verified Answer
Answer
The solutions are \( m = \sqrt{17} \) and \( m = -\sqrt{17} \).
Solution
To solve m² = 17 using the square root property, follow these steps:
1. Start with the equation:
m² = 17
2. Take the square root of both sides, remembering that both the positive and negative square roots are valid:
m = ±√17
So, the solutions are:
m = √17 and m = –√17
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Simplify this solution Extra Insights
To solve the equation \( \mathrm{m}^{2}=17 \) using the square root property, we take the square root of both sides. This gives us \( \mathrm{m} = \sqrt{17} \) or \( \mathrm{m} = -\sqrt{17} \). This means the solutions are approximately \( 4.12 \) and \( -4.12 \) since \( \sqrt{17} \) is about \( 4.123 \) when calculated. This property is particularly handy in algebra and helps simplify equations quickly. However, a common mistake is forgetting to consider both the positive and negative square roots when solving equations—they could lead to missing potential solutions, especially in quadratic equations! So, always remember to check for both!
