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

Question

49 > 7
−− √
49 < 7
−− √
48 <
−− √ 36
−− √
48 >
−− √ 36
−−

Answer 1

To evaluate the statements using rational approximations, let's calculate each square root involved:

1. √49 = 7: This is accurate, so the statement \(49 > \sqrt{49}\) is true.

2. √48: The square root of 48 is approximately \(6.928\) (since \(6.928^2 \approx 48\)).

3. √36 = 6: This is accurate, so we can evaluate \(48 < \sqrt{36}\) and \(48 > \sqrt{36}\):

   • \(48 < 6\) is false.
   • \(48 > 6\) is true.

Now let’s summarize the findings of the statements:

• \(49 > \sqrt{49}\): True
• \(49 < \sqrt{49}\): False
• \(48 < \sqrt{36}\): False
• \(48 > \sqrt{36}\): True

Therefore, the statements that are true are:

1. \(49 > \sqrt{49}\)
2. \(48 > \sqrt{36}\)

Given that you are likely looking for just one correct statement, the true statements are \(49 > \sqrt{49}\) and \(48 > \sqrt{36}\).

In summary, the correct statement is:

1. \(49 > \sqrt{49}\) is true.
2. \(48 > \sqrt{36}\) is true.

Based on this assessment, the final answer for the question would be:

• 49 > √49 is true.