Using rational approximations what statement is true would it be square root of 49 is less than seven or square root of 48 is less than square root of 36 or would it be square root of 49 is greater than seven or square root of 48 is greater than square root of 36

1 answer

To determine the truth of these statements, we can evaluate each one:

  1. Square root of 49 is less than seven: \[ \sqrt{49} = 7 \] This statement is false because \(\sqrt{49}\) is equal to 7, not less than.

  2. Square root of 48 is less than square root of 36: \[ \sqrt{48} \approx 6.928 \quad \text{and} \quad \sqrt{36} = 6 \] This statement is also false because \(\sqrt{48}\) is approximately 6.928, which is greater than 6.

  3. Square root of 49 is greater than seven: As mentioned, \(\sqrt{49} = 7\), so this statement is false.

  4. Square root of 48 is greater than square root of 36: \[ \sqrt{48} \approx 6.928 \quad \text{and} \quad \sqrt{36} = 6 \] This statement is true because \(\sqrt{48} \approx 6.928\) is indeed greater than 6.

Therefore, the true statement among the given options is:

Square root of 48 is greater than square root of 36.