Using rational approximations, what statement is true?

Question

A. √48 < 7
B. √ 49 > 7
C. √ 48 < √36
D. √ 48 > √ 36

Answer 1

Let's evaluate the statements one by one using rational approximations.

1. A. $\sqrt{48}<7$
   We know that $7^2=49$, and since $48<49$, this means $\sqrt{48}<7$ is true.

2. B. $\sqrt{49}>7$
   Since $\sqrt{49}=7$, this means $\sqrt{49}>7$ is false.

3. C. $\sqrt{48}<\sqrt{36}$
   Since $\sqrt{36}=6$, we need to determine if $\sqrt{48}<6$. Since $48>36$, it follows that $\sqrt{48}>\sqrt{36}$, thus this statement is false.

4. D. $\sqrt{48}>\sqrt{36}$
   Since $\sqrt{48}>\sqrt{36}$ is true, because $48>36$.

Based on this analysis, the true statements are:

• A. $\sqrt{48}<7$ (True)
• D. $\sqrt{48}>\sqrt{36}$ (True)

Therefore, both statements A and D are true.

Answer 2

Only one can true

Answer 3

Thank you for your clarification. Let's evaluate each statement again more clearly to identify the unique true statement.

1. A. $\sqrt{48}<7$
   Since $7^2=49$ and $48<49$, it follows that $\sqrt{48}<7$ is true.

2. B. $\sqrt{49}>7$
   $\sqrt{49}=7$, so this statement is false.

3. C. $\sqrt{48}<\sqrt{36}$
   Since $\sqrt{36}=6$ and $48>36$, it follows that $\sqrt{48}>\sqrt{36}$, so this statement is false.

4. D. $\sqrt{48}>\sqrt{36}$
   Since $\sqrt{48}>\sqrt{36}$ is true, because $48>36$.

Given that we are to identify only one true statement from the provided options, we must choose between (A) and (D) based on comparison values.

In summary:

• A is true: $\sqrt{48}<7$
• D is true: $\sqrt{48}>\sqrt{36}$

Since both A and D are true, this seems to contradict your directive of having only one true statement. Therefore, if we need to determine which is likely meant to hold over context or preference, we might interpret:

• A. $\sqrt{48}<7$ can be viewed as "common knowledge," while D clearly states a relationship based directly on the square roots.

However, if strictly limited to select only one statement to consider as a valid answer in competitive clarifications:

• Priority of proximity to 7 makes A stronger in typical affirmative checks.

Thus, based on your criteria of only one being true and the checks made, A. $\sqrt{48}<7$ holds to be preferred as the singular noteworthy true statement if forced to prioritization.

If this isn't aligning with your specified criteria or nuances from the context of evaluation, please advise on further context or constraints.