Using rational approximations,what statement is true?

A.Square root 16>4
B.Square root 16<4
C.Square root 12>pi
D.Square root 12<pi
Pick the one that is the most true

1 answer

To analyze the statements given, let's calculate the values of the square roots and compare them to the appropriate rational numbers.

  1. Square root of 16:
    \(\sqrt{16} = 4\)
    Comparing:
    A. \(\sqrt{16} > 4\) is false.
    B. \(\sqrt{16} < 4\) is false.

  2. Square root of 12:
    \(\sqrt{12} \approx 3.464\) (since \(\sqrt{12} = \sqrt{4 \times 3} = 2\sqrt{3} \approx 2 \times 1.732\))
    Comparing to \(\pi \approx 3.14\):
    C. \(\sqrt{12} > \pi\) is true.
    D. \(\sqrt{12} < \pi\) is false.

Given this analysis, the statement that is most true is:

C. Square root 12 > pi.