To evaluate the provided statements using rational approximations, we can analyze each one:
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The square root of 48 > the square root of 36
- The square root of 36 is \(6\) (since \(6^2 = 36\)).
- The square root of 48 is approximately \(6.93\) (since \(6.93^2 \approx 48\)).
- So, \( \sqrt{48} > \sqrt{36} \) is true.
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The square root of 49 < 7
- The square root of 49 is \(7\) (since \(7^2 = 49\)).
- So, \( \sqrt{49} < 7 \) is false.
-
The square root of 48 < the square root of 36
- Since we established that \( \sqrt{48} > \sqrt{36} \), this statement is false.
-
The square root of 49 > 7
- Since \( \sqrt{49} = 7 \), this statement is false.
Therefore, the only true statement is: The square root of 48 > the square root of 36.