Question

Using rational approximations, what statement is true?(1 point) Responses 71−−√>61−−√ start root 71 end root greater than start root 61 end root 71 −−−√<61−−√ start root 71 end root less than start root 61 end root 81−−√<9 start root 81 end root less than 9 81−−√>9

Answer 1

To determine which of the statements is true, let's approximate the square roots involved in each option:

1. $\sqrt{71}$ and $\sqrt{61}$

   • $\sqrt{71}$ is approximately $8.426$
   • $\sqrt{61}$ is approximately $7.810$
   • Thus, $\sqrt{71}>\sqrt{61}$

2. Comparing $\sqrt{81}$ and $9$

   • $\sqrt{81}=9$
   • Therefore, $\sqrt{81}$ is equal to $9$

Given these calculations, the true statements from the options provided are:

• $\sqrt{71}>\sqrt{61}$
• $\sqrt{81}=9$ (neither $<$ nor $>$)

So the valid answer from your options is:

• $\sqrt{71}>\sqrt{61}$

The other statements can be evaluated, but this one is definitely true.

Answer 2

u sure

Answer 3

Let’s go through the comparisons again step by step to ensure accuracy.

1. For $\sqrt{71}$ and $\sqrt{61}$:

   • We know that $71>61$. Since the square root function is monotonically increasing, this implies: $$\sqrt{71}>\sqrt{61}$$

2. For $\sqrt{81}$:

   • $\sqrt{81}=9$. When comparing $\sqrt{81}$ with $9$: $$\sqrt{81}=9$$
   • Therefore, it is incorrect to say $\sqrt{81}<9$ or $\sqrt{81}>9$. The correct statement is $\sqrt{81}=9$.

Summary of Findings:

• The statement $\sqrt{71}>\sqrt{61}$ is true.
• The statement $\sqrt{81}<9$ is false.
• The statement $\sqrt{81}>9$ is false.
• The statement $\sqrt{81}<9$ is false.

Thus, the only correct statement among the options you provided is indeed:

• $\sqrt{71}>\sqrt{61}$.

Although I initially stated that one of the options would also state an equality involving $9$, the key takeaway is that $\sqrt{71}>\sqrt{61}$ is definitively true. Thank you for your patience!