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

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

1 answer

To evaluate the given statements and determine which one is true using rational approximations, let's compute the approximate values of the square roots:

  1. For \( \sqrt{36} \):

    • \( \sqrt{36} = 6 \)
  2. For \( \sqrt{49} \):

    • \( \sqrt{49} = 7 \)

Next, we can check each statement:

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

    • \( 48 > 6 \) is true.
  2. \( \sqrt{49} < 7 \)

    • \( 7 < 7 \) is false.
  3. 48 < \( \sqrt{36} \)

    • \( 48 < 6 \) is false.
  4. \( \sqrt{49} > 7 \)

    • \( 7 > 7 \) is false.

From these computations, the only statement that is true is:

48 > \( \sqrt{36} \).