Question

1. fill in the blank with the correct inequality symbol: 2\sqrt{40} ____ 7 + \sqrt{63}

Explanation:

Step1: Approximate $2\sqrt{40}$

First, $\sqrt{40}\approx 6.32$ (since $6.32^2 = 39.9424$), then $2\sqrt{40}\approx 2\times6.32 = 12.64$.

Step2: Approximate $7+\sqrt{63}$

$\sqrt{63}\approx 7.94$ (since $7.94^2=63.0436$), then $7 + \sqrt{63}\approx7 + 7.94=14.94$.

Step3: Compare the two - values

Since $12.64<14.94$, we have $2\sqrt{40}<7 + \sqrt{63}$.

Answer:

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