Question

Fill in the blanks with two consecutive integers to complete the following inequality.

Answer 1

Answer:

9 < √97 < 10

Step-by-step explanation:

√97 is a little less than √100

Which is 10

9 < √97 < 10

Answer 2

Answer:  9 < √97 < 10

=====================================================

Explanation:

Consider that 81 < 97 < 100 is a true statement. Note the 81 and 100 are perfect squares such that 81 = 9^2 and 100 = 10^2

We can apply the square root to all three sides to get the following

$81 < 97 < 100\\\\\sqrt{81} < \sqrt{97} < \sqrt{100}\\\\\sqrt{9^2} < \sqrt{97} < \sqrt{10^2}\\\\9 < \sqrt{97} < 10\\\\\text{The number }\sqrt{97} \text{ is between 9 and 10}$

Using a calculator, we can help verify this

$\sqrt{97} \approx 9.85$