Using rational approximations, what statement is true?(1 point)

Question

Responses

49−−√>7
start root 49 end root greater than 7

49−−√<7
start root 49 end root less than 7

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
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Answer 1

To evaluate the statements, we can find the square roots of the numbers involved:

1. \(\sqrt{49}\):

   • This is equal to 7.

2. \(\sqrt{48}\):

   • The approximate value of \(\sqrt{48}\) is around 6.93 since \(\sqrt{48} \approx 6.928\).

3. \(\sqrt{36}\):

   • This is equal to 6.

Now, let's evaluate each statement:

1. \(\sqrt{49} > 7\):

   • This is false, as \(\sqrt{49} = 7\).

2. \(\sqrt{49} < 7\):

   • This is also false, as \(\sqrt{49} = 7\).

3. \(\sqrt{48} > \sqrt{36}\):

   • Since \(\sqrt{48} \approx 6.928\) and \(\sqrt{36} = 6\), this is true.

4. \(\sqrt{48} < \sqrt{36}\):

   • This is false because, as established, \(\sqrt{48} \approx 6.928\) which is greater than 6.

Therefore, the true statement is: \[ \sqrt{48} > \sqrt{36} \]