Estimate the square root between two consecutive whole numbers.
$\sqrt{138}$

• A. Between $11$ and $12$
• B. Between $10$ and $11$
• C. Between $10$ and $12$
• D. Between $11$ and $13$

Answer: (A)

Verified step by step guidance

1. Identify the two consecutive whole numbers between which the square root of 138 lies by finding perfect squares closest to 138.
2. Recall that a perfect square is a number that is the square of an integer, such as \(\ 11^2 = 121 \ \) and \(\ 12^2 = 144 \ \).
3. Compare 138 with these perfect squares: since \(\ 121 < 138 < 144 \ \), the square root of 138 must be between 11 and 12.
4. Understand that because 138 is closer to 144 than to 121, the square root of 138 will be closer to 12 than to 11, but still between these two numbers.
5. Conclude that the square root of 138 is between the consecutive whole numbers 11 and 12.