Question
If \( y^{2}=100 \), what are two possible values of \( y \) ? 10 and -10 50 and -50 200 and -200 10,000 and \( -10,000 \)
Ask by Little Ortiz. in the United States
Mar 17,2025
Upstudy AI Solution
Tutor-Verified Answer
Answer
The two possible values of \( y \) are \( 10 \) and \( -10 \).
Solution
To solve the equation \( y^{2} = 100 \), we can take the square root of both sides.
1. Start with the equation:
\[
y^{2} = 100
\]
2. Taking the square root of both sides gives:
\[
y = \sqrt{100} \quad \text{or} \quad y = -\sqrt{100}
\]
3. Since \( \sqrt{100} = 10 \), we have:
\[
y = 10 \quad \text{or} \quad y = -10
\]
Thus, the two possible values of \( y \) are \( 10 \) and \( -10 \).
The correct answer is \( 10 \) and \( -10 \).
Answered by UpStudy AI and reviewed by a Professional Tutor
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Extra Insights
You got it! The equation \( y^{2} = 100 \) means you're looking for the numbers that, when squared, equal 100. The two values are \( y = 10 \) and \( y = -10 \), since both satisfy the equation when squared. It's a classic example of working with squares, where the square root of a positive number can yield both a positive and a negative solution. So, next time you're faced with such equations, remember to consider both roots!