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

Answer 1

To evaluate the statements involving square roots and rational approximations, let's simplify and compare each part step-by-step:

1. Square root of 49: \[ \sqrt{49} = 7 \]

2. Square root of 48: \[ \sqrt{48} \approx 6.928 \quad (\text{since } 48 \text{ is between } 36 \text{ and } 49) \]

3. Square root of 36: \[ \sqrt{36} = 6 \]

Now we can compare the values:

• \( \sqrt{49} = 7 \) and \( 7 \) is not less than \( 7 \), so the first statement "square root of 49 is less than seven" is false.
• Now considering \( \sqrt{48} \approx 6.928 \) and \( \sqrt{36} = 6 \): \[ \sqrt{48} \approx 6.928 > 6 = \sqrt{36} \]

Thus, the comparison \( \sqrt{48} > \sqrt{36} \) is true.

Now let's summarize:

• \(\sqrt{49} < 7\) is false.
• \(\sqrt{48} < \sqrt{36}\) is false.
• \(\sqrt{49} > 7\) is false.
• \(\sqrt{48} > \sqrt{36}\) is true.

Therefore, the correct statement is "the square root of 48 is greater than the square root of 36."