Without plotting these numbers, decide which inequalities are true. Check all that apply. $$ \sqrt{7}2 $$ $$ \sqrt{7}

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Without plotting these numbers, decide which inequalities are true. Check all that apply. $$ \sqrt{7}>2 $$ $$ \sqrt{7}<7 $$ $$ \sqrt{7}<\sqrt{8} $$ $$ \sqrt{8}<2 $$ $$ \sqrt{8}<8 $$ $$ \square $$

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1. Evaluate $$ \sqrt{7} $$. - Since $$ 2^2 = 4 $$ and $$ 3^2 = 9 $$, we know $$ 2 < \sqrt{7} < 3. $$ - More precisely, $$ \sqrt{7} \approx 2.646 $$. 2. Evaluate $$ \sqrt{8} $$. - Since $$ 2^2 = 4 $$ and $$ 3^2 = 9 $$, we know $$ 2 < \sqrt{8} < 3. $$ - More precisely, $$ \sqrt{8} \approx 2.828 $$. 3. Check each inequality: - $$ \sqrt{7} > 2 $$ Since $$ 2.646 > 2 $$, this inequality is **true**. - $$ \sqrt{7} < 7 $$ Since $$ 2.646 < 7 $$, this inequality is **true**. - $$ \sqrt{7} < \sqrt{8} $$ Since $$ 2.646 < 2.828 $$, this inequality is **true**. - $$ \sqrt{8} < 2 $$ Since $$ 2.828 > 2 $$, this inequality is **false**. - $$ \sqrt{8} < 8 $$ Since $$ 2.828 < 8 $$, this inequality is **true**. The true inequalities are: $$ \sqrt{7}>2,\quad \sqrt{7}<7,\quad \sqrt{7}<\sqrt{8},\quad \sqrt{8}<8. $$ The true inequalities are: - $$ \sqrt{7} > 2 $$ - $$ \sqrt{7} < 7 $$ - $$ \sqrt{7} < \sqrt{8} $$ - $$ \sqrt{8} < 8 $$

Without plotting these numbers, decide which inequalities are true. Check all that apply. \( \sqrt{7}>2 \) \( \sqrt{7}<7 \) \( \sqrt{7}<\sqrt{8} \) \( \sqrt{8}<2 \) \( \sqrt{8}<8 \) \( \square \)

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