Question

question
between which two consecutive whole numbers does $sqrt{44}$ lie? fill out the sentence below to justify your answer and use your mouse to drag $sqrt{44}$ 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 $sqrt{44}$ is between $square$ and $square$.
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Explanation:

Step1: Find perfect squares around 44

We know that \(6^2 = 36\) and \(7^2 = 49\).

Step2: Compare with \(\sqrt{44}\)

Since \(36<44<49\), taking square roots (and since square root is an increasing function for non - negative numbers), we have \(\sqrt{36}<\sqrt{44}<\sqrt{49}\).

Step3: Simplify the square roots

\(\sqrt{36} = 6\) and \(\sqrt{49}=7\). So \(\sqrt{44}\) is between 6 and 7.

Answer:

Since \(\sqrt{\boldsymbol{36}}=\boldsymbol{6}\) and \(\sqrt{\boldsymbol{49}}=\boldsymbol{7}\), it is known that \(\sqrt{44}\) is between \(\boldsymbol{6}\) and \(\boldsymbol{7}\).