Select the correct classifications for √32.

Question

? number
rational
irrational
? decimal
repeating
non-repeating
terminating

Answer 1

To classify \( \sqrt{32} \):

1. Type of number:

   • \( \sqrt{32} \) is approximately \( 5.656854 \), which is not a perfect square. Therefore, it is an irrational number.

2. Decimal classification:

   • As an irrational number, the decimal representation of \( \sqrt{32} \) is non-repeating and non-terminating. Therefore, it is a non-repeating decimal.

In summary:

• Number type: irrational
• Decimal: non-repeating

Answer 2

Find the sum and then classify it. 5/6 + √91 (1 point) Responses 10.3¯¯¯10.3¯, rational 10 point repeating 3, rational 91.83¯¯¯91.83¯, rational 91 point 8 repeating 3, rational 10.3727253…10.3727253…, irrational 10 point 3 7 2 7 2 5 3 dots, irrational 9.58297100…9.58297100…, irrational

Answer 3

To find the sum of \( \frac{5}{6} + \sqrt{91} \), we first need to evaluate each component:

1. Calculate \( \sqrt{91} \):

   • The approximate value of \( \sqrt{91} \) is around \( 9.539 \). (More precise calculations yield a value of around 9.539392)

2. Calculate \( \frac{5}{6} \):

   • The value of \( \frac{5}{6} = 0.8333... \)

3. Now sum them: \[ \frac{5}{6} + \sqrt{91} \approx 0.8333 + 9.539 \approx 10.372725... \]

Classification of the Sum

• Type of Number:

  • \( \sqrt{91} \) is irrational. Adding a rational number (\( \frac{5}{6} \)) to an irrational number results in an irrational number.

• Decimal Classification:

  • The decimal representation \( 10.3727253… \) is non-repeating and non-terminating, confirming that it is also irrational.

Conclusion

The sum \( \frac{5}{6} + \sqrt{91} \approx 10.3727253... \) is classified as irrational.