So we need to find the bounds of our answer. If we cube 30, we get 27,000, which definitely does not fit our criteria. However, 20 cubed is 8000, so our answer is probably just a little more than 20. [tex]21^3[/tex]= 9261, [tex]22^3[/tex]= 10648. We have found out answer: [tex]21^3=9261[/tex]
Answer:9261
Step-by-step explanation:
To find the greatest 4-digit number that is a perfect cube, we need to determine the cube root of the largest 4-digit number, which is 9999.
First, we approximate the cube root of 9999:
\[ \sqrt[3]{9999} \approx 21.5 \]
We check the cube of 21 and 22, the nearest integers to 21.5.
Calculating the cube of 22:
\[ 22^3 = 22 \times 22 \times 22 = 484 \times 22 = 10648 \]
10648 is greater than 9999, so it is not a 4-digit number.
Calculating the cube of 21:
\[ 21^3 = 21 \times 21 \times 21 = 441 \times 21 = 9261 \]
9261 is a 4-digit number and less than 9999.
Thus, the greatest 4-digit number that is a perfect cube is:
\[ \boxed{9261} \]