Question

Using rational approximations, what statement is true?(1 point) Responses 3 > 9–√ 3 > 9–√ π < 9–√ π < 9–√ π > 9–√ π > 9–√ 3 < 9–√

Answer 1

To determine which statement is true using rational approximations, we can evaluate the expressions involving \(\sqrt{9}\), \(\pi\), and \(3\):

1. \(\sqrt{9} = 3\)
2. \(\pi \approx 3.14\)

Now we compare the values:

- \(3\) (which is equal to \(\sqrt{9}\))
- \(\pi \approx 3.14\)

Now we can analyze the statements:

- \(3 > \sqrt{9}\) : This is **false** because they are equal.
- \(\sqrt{3} > 3\) : This is also **false** because \(\sqrt{3} \approx 1.73\).
- \(\pi < \sqrt{9}\) : This is **false** (as mentioned \(\pi \approx 3.14\) and \(\sqrt{9} = 3\)).
- \(\pi < 3\) : This is **false**.
- \(\pi > \sqrt{9}\) : This is **true** because \(\pi \approx 3.14\) and \(\sqrt{9} = 3\).
- \(3 < \sqrt{9}\) : This is **false** (as they are equal).

The true statement using rational approximations is:
\(\pi > \sqrt{9}\).