Question:
Given that \( st = \sqrt{10} \). Compare:
Quantity A: \( s^2 \)
Quantity B: \( \dfrac{10}{t^2} \)
Given that \( st = \sqrt{10} \). Compare:
Quantity A: \( s^2 \)
Quantity B: \( \dfrac{10}{t^2} \)
Quantity A: \( s^2 \)
Quantity B: \( \dfrac{10}{t^2} \)
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When given a product like \( st \), squaring it often helps to compare squared terms such as \( s^2 \) and \( t^2 \).
Updated On: Oct 7, 2025
- Quantity A is greater.
- Quantity B is greater.
- The two quantities are equal.
- The relationship cannot be determined from the information given.
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The Correct Option is C
Solution and Explanation
Step 1: Start with the given relation.
It is given that \( st = \sqrt{10} \). Squaring both sides, we get: \[ (st)^2 = (\sqrt{10})^2 \quad \Rightarrow \quad s^2 t^2 = 10. \] Step 2: Isolate \( s^2 \).
Dividing both sides of the equation by \( t^2 \), we get: \[ s^2 = \frac{10}{t^2}. \] Step 3: Compare.
From this expression, it is clear that Quantity A and Quantity B are identical.
Step 4: Conclusion.
Therefore, \[ \boxed{\text{(C) The two quantities are equal.}} \]
It is given that \( st = \sqrt{10} \). Squaring both sides, we get: \[ (st)^2 = (\sqrt{10})^2 \quad \Rightarrow \quad s^2 t^2 = 10. \] Step 2: Isolate \( s^2 \).
Dividing both sides of the equation by \( t^2 \), we get: \[ s^2 = \frac{10}{t^2}. \] Step 3: Compare.
From this expression, it is clear that Quantity A and Quantity B are identical.
Step 4: Conclusion.
Therefore, \[ \boxed{\text{(C) The two quantities are equal.}} \]
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