Question

What two integers is the square root of 12 between ? How do you know ?


Please explain how you know along with the answer.

Answer 1

Answer:  Between 3 and 4.

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Explanation:

The value 12 is between the perfect squares 9 and 16

This means we can write the following inequality $9 < 12 < 16$

From here we apply the square root to all three sides and simplify like so

$9 < 12 < 16\\\\\sqrt{9} < \sqrt{12} < \sqrt{16}\\\\3 < \sqrt{12} < 4$

and we see that the square root of 12 is between 3 and 4.

Using a calculator would confirm this

$\sqrt{12} \approx 3.464$

Answer 2

Answer:

Step-by-step explanation:

Find the numbers closest to 12 on either side that are perfect squares:

1, 4, 9, 16, 25

12 is in between the numbers 9 and 16. The square root of 9 is 3 and the square root of 16 is 4. Therefore, the square root of 12 is in between 3 and 4.