Question

Using rational approximations, what statement is true?
A. √49 < 7
B. √ 49 > 7
C. √ 48 < √36
D. √ 48 > √ 36

Answer 1

To determine which statement is true using rational approximations, let's analyze each option:

A. \( \sqrt{49} < 7 \): This is false because \( \sqrt{49} = 7 \).

B. \( \sqrt{49} > 7 \): This is false since \( \sqrt{49} = 7 \).

C. \( \sqrt{48} < \sqrt{36} \): To evaluate this, we can observe that \( \sqrt{48} \) is approximately \( 6.93 \) (since \( \sqrt{49} = 7 \) and \( 48 \) is just under \( 49 \)), and \( \sqrt{36} = 6 \). Therefore, \( \sqrt{48} > \sqrt{36} \), making this statement false.

D. \( \sqrt{48} > \sqrt{36} \): Following the calculation from C, \( \sqrt{48} \approx 6.93 \) and \( \sqrt{36} = 6 \), which confirms that \( \sqrt{48} > \sqrt{36} \), making this statement true.

So the correct answer is **D. \( \sqrt{48} > \sqrt{36} \)**.