Question

complete the following statement. use the integers that are closest to the number in the middle.
□ < sqrt3{20} < □

Explanation:

Step1: Find nearest lower cube

Identify the largest integer whose cube is less than 10.
$2^3 = 8$, and $8 < 10$

Step2: Find nearest upper cube

Identify the smallest integer whose cube is greater than 10.
$3^3 = 27$, and $27 > 10$

Step3: Relate to cube root

Since $2^3 < 10 < 3^3$, take cube roots of all parts.
$\sqrt[3]{2^3} < \sqrt[3]{10} < \sqrt[3]{3^3}$ which simplifies to $2 < \sqrt[3]{10} < 3$

Answer:

$2 < \sqrt[3]{10} < 3$