Estimate $\sqrt[3]{923}$ to the nearest integer. \[ \sqrt[3]{923} \approx \]

Step 1 ：Estimate the cube root of 923 to the nearest integer.

Step 2 ：Calculate the cube root of 923, which is approximately 9.736448409747753.

Step 3 ：Round the cube root to the nearest integer, which gives us 10.

Step 4 ：Final Answer: \(\boxed{10}\)