using rational approximations what statement is true

Question

A. 3< square root 9
B. 3 > square root 9
C. pi < square root 9
D. pi > square root 9

Answer 1

To determine which statement is true using rational approximations, let's evaluate the square root of 9 and also consider the approximation of π (pi).

1. Square root of 9:
   \(\sqrt{9} = 3\)

2. Approximating π:
   The approximate value of π is about 3.14.

Now let's evaluate each statement:

A. \(3 < \sqrt{9}\)
This is false because \(\sqrt{9} = 3\).

B. \(3 > \sqrt{9}\)
This is also false because \(\sqrt{9} = 3\).

C. \(\pi < \sqrt{9}\)
This is false because \(3.14 > 3\).

D. \(\pi > \sqrt{9}\)
This is true because \(3.14 > 3\).

Thus, the true statement is:

D. \(\pi > \sqrt{9}\).