Question

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

? < √97 < ?

Answer 1

Answer: 9 < √97 < 10

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Step-by-step 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\\\\√(81) < √(97) < √(100)\\\\√(9^2) < √(97) < √(10^2)\\\\9 < √(97) < 10\\\\\text{The number }√(97) \text{ is between 9 and 10}\\\\`

Using a calculator, we can help verify this

`√(97) \approx 9.85`

Answer 2

9 < √97 < 10

Step-by-step explanation:

√97 is a little less than √100

Which is 10

9 < √97 < 10