9. Using rational approximations, what is an inequality statement comparing √64 and √59.

The inequality is: v64 √59

3 answers

To compare \(\sqrt{64}\) and \(\sqrt{59}\) using rational approximations, we can start by calculating the values of these square roots.

  1. We know that: \[ \sqrt{64} = 8 \]

  2. For \(\sqrt{59}\), we can use a rational approximation:

    • We know \(\sqrt{49} = 7\) and \(\sqrt{64} = 8\), so \(\sqrt{59}\) is between 7 and 8.
    • To get a more accurate approximation, we can estimate by checking perfect squares around 59:
      • \( 7.5^2 = 56.25 \)
      • \( 7.6^2 = 57.76 \)
      • \( 7.7^2 = 59.29 \)

    Since \( 7.6^2 < 59 < 7.7^2 \), we can conclude that: \[ 7.6 < \sqrt{59} < 7.7 \]

  3. Hence, we can place \(\sqrt{59}\) approximately between 7.6 and 7.7.

Now we can compare: \[ \sqrt{64} = 8 \quad \text{and} \quad 7.6 < \sqrt{59} < 7.7 \]

Thus, the inequality statement comparing \(\sqrt{64}\) and \(\sqrt{59}\) is: \[ \sqrt{64} > \sqrt{59} \]

The final inequality statement is: \[ 8 > \sqrt{59} \]

wat iz da anwsr?

The answer is:

\(\sqrt{64} > \sqrt{59}\)

This means that \(\sqrt{64}\) (which is 8) is greater than \(\sqrt{59}\).