Question

Using rational approximations, what statement is true?(1 point) Responses 48−−√<36−−√ start root 48 end root less than start root 36 end root 48−−√>36−−√ start root 48 end root greater than start root 36 end root 49−−√>7 start root 49 end root greater than 7 49−−√<7 ...

Answer 1

To compare the expressions involving square roots, we can find the approximate values of the square roots:

1. \(\sqrt{48}\) is approximately \(6.9282\) and \(\sqrt{36} = 6\).
2. \(\sqrt{49} = 7\).

Now let's evaluate the statements:

1. \(\sqrt{48} < \sqrt{36}\) is false because \(6.9282 > 6\).
2. \(\sqrt{48} > \sqrt{36}\) is true because \(6.9282 > 6\).
3. \(\sqrt{49} > 7\) is false because \(\sqrt{49} = 7\).
4. \(\sqrt{49} < 7\) is false because \(\sqrt{49} = 7\).

So the true statement is: \(\sqrt{48} > \sqrt{36}\).