Question

1. devin got an answer of about 4.36 when she entered 19 on her calculator and pressed the (√) key. which of the following statements best describes whether or not devins answer was reasonable? a. it is reasonable, because 19 is an odd number. b. it is reasonable, because 4 squared is 16 and 5 squared is 25. c. it is not reasonable, because the answer should only be slightly less than 5. d. it is not reasonable, because the answer should be a whole number.

Explanation:

Step1: Recall square root concept

The square root of a number \( x \) (denoted \( \sqrt{x} \)) is a value \( y \) such that \( y^2 = x \). We know the perfect squares around 19: \( 4^2 = 16 \) and \( 5^2 = 25 \).

Step2: Analyze the square root of 19

Since \( 16 < 19 < 25 \), taking square roots (which is an increasing function for non - negative numbers), we have \( \sqrt{16}<\sqrt{19}<\sqrt{25} \), so \( 4 < \sqrt{19}<5 \). The value 4.36 is between 4 and 5, so we can check the options:

• Option A: The parity (odd/even) of 19 has nothing to do with the value of its square root. So A is incorrect.
• Option B: Since \( 4^2 = 16 \) and \( 5^2 = 25 \), and \( 16<19<25 \), \( \sqrt{19} \) should be between 4 and 5. 4.36 is between 4 and 5, so this explanation is correct.
• Option C: The statement says it is not reasonable, but 4.36 is slightly less than 5 (since 5 - 4.36 = 0.64) and between 4 and 5, so the answer is reasonable. So C is incorrect.
• Option D: 19 is not a perfect square, so \( \sqrt{19} \) is not a whole number. So D is incorrect.

Answer:

B. It is reasonable, because 4 squared is 16 and 5 squared is 25.