using rational approximations what statement is true

Question

√49 > 7
√49 < 7
√48 < √36
√48 > √36

Answer 1

To evaluate the statements using rational approximations:

1. √49 > 7: This is false because \(\sqrt{49} = 7\).
2. √49 < 7: This is also false because \(\sqrt{49} = 7\).
3. √48 < √36: This is false because \(\sqrt{48} \approx 6.928\) and \(\sqrt{36} = 6\), so \(\sqrt{48} > \sqrt{36}\).
4. √48 > √36: This is true because \(\sqrt{48} \approx 6.928\) and \(\sqrt{36} = 6\).

So, the true statement is √48 > √36.