Question

question
between which two consecutive whole numbers does \\(\sqrt{18}\\) lie? fill out the sentence below to justify your answer and use your mouse to drag \\(\sqrt{18}\\) to an approximately correct location on the number line.
answer attempt 1 out of 2
since \\(\sqrt{\square}=\square\\) and \\(\sqrt{\square}=\square\\) it is known that \\(\sqrt{18}\\) is between \\(\square\\) and \\(\square\\).
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Explanation:

Step1: Find perfect squares around 18

We know that \( \sqrt{16} = 4 \) and \( \sqrt{25} = 5 \) because \( 4^2 = 16 \) and \( 5^2 = 25 \).

Step2: Compare with \( \sqrt{18} \)

Since \( 16 < 18 < 25 \), taking square roots (which is a monotonically increasing function for non - negative numbers), we have \( \sqrt{16}<\sqrt{18}<\sqrt{25} \), that is \( 4 < \sqrt{18}<5 \).

Answer:

Since \( \sqrt{16} = 4 \) and \( \sqrt{25}=5 \), it is known that \( \sqrt{18} \) is between \( 4 \) and \( 5 \).