Question

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

Answer 1

To determine which inequalities are true using rational approximations, we can evaluate the square roots involved.

1. Comparing \(\sqrt{48}\) and \(\sqrt{36}\):

   • \(\sqrt{36} = 6\)
   • \(\sqrt{48} \approx 6.928\) (since \(\sqrt{48} = \sqrt{16 \cdot 3} = 4\sqrt{3} \approx 4 \times 1.732 \approx 6.928\))

   Since \(6.928 > 6\), we have: \[ \sqrt{48} > \sqrt{36} \]

2. Comparing \(\sqrt{49}\) and \(7\):

   • \(\sqrt{49} = 7\)

   Hence, we have: \[ \sqrt{49} = 7 \]

From our evaluations, the true statements are:

• \(\sqrt{48} > \sqrt{36}\)
• \(\sqrt{49} = 7\)

Thus, the true statement among the options provided is: \[ \sqrt{48} > \sqrt{36} \quad \text{(first option)} \]

Therefore, the correct response is: \(\sqrt{48} > \sqrt{36}\).