1. The problem asks to identify which of the given inequalities involving square roots is incorrect. 2. Recall that the square root function gives the positive number whose square is the given number. 3. Let's evaluate each inequality: - For $9 < \sqrt{90} < 10$: - $9^2 = 81$ and $10^2 = 100$ - Since $90$ is between $81$ and $100$, $\sqrt{90}$ is between $9$ and $10$. This is correct. - For $5 < \sqrt{37} < 6$: - $5^2 = 25$ and $6^2 = 36$ - Since $37$ is greater than $36$, $\sqrt{37}$ is greater than $6$, so this inequality is incorrect. - For $1 < \sqrt{2} < 2$: - $1^2 = 1$ and $2^2 = 4$ - Since $2$ is between $1$ and $4$, $\sqrt{2}$ is between $1$ and $2$. This is correct. - For $14 < \sqrt{210} < 15$: - $14^2 = 196$ and $15^2 = 225$ - Since $210$ is between $196$ and $225$, $\sqrt{210}$ is between $14$ and $15$. This is correct. 4. Therefore, the incorrect statement is $5 < \sqrt{37} < 6$. Final answer: The incorrect inequality is $5 < \sqrt{37} < 6$.