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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

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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 \( -10 \).

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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!

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