To determine whether the product of the square root of 49 and \( \frac{1}{3} \) is rational or irrational, we can follow these steps:
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Evaluate the square root of 49: \[ \sqrt{49} = 7 \]
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Multiply by \( \frac{1}{3} \): \[ 7 \times \frac{1}{3} = \frac{7}{3} \]
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Check whether \( \frac{7}{3} \) is rational: A number is rational if it can be expressed as a fraction of two integers. Since both 7 and 3 are integers, \( \frac{7}{3} \) is indeed a rational number.
Conclusion:
The product of the square root of 49 and \( \frac{1}{3} \) is rational.