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!