Which of the following is an irrational number between 5 and 7: √6, √12, √27, √36 ?

Answer 1

To determine which of the given options is an irrational number between 5 and 7, let's evaluate each square root:

1. \( \sqrt{6} \)

   • Approximately \( 2.45 \) (since \( 2.45^2 \approx 6 \)).
   • Not in the range of 5 to 7.

2. \( \sqrt{12} \)

   • Approximately \( 3.46 \) (since \( 3.46^2 \approx 12 \)).
   • Not in the range of 5 to 7.

3. \( \sqrt{27} \)

   • Approximately \( 5.2 \) (since \( 5.2^2 \approx 27 \)).
   • This is between 5 and 7.

4. \( \sqrt{36} \)

   • Exactly \( 6 \).
   • This is also between 5 and 7, but it is a rational number.

From the options provided, the only irrational number that falls between 5 and 7 is \( \sqrt{27} \).