Question

complete the following statement. use the integers that are closest to the number in the middle.
$\square < \sqrt3{74} < \square$

Explanation:

Step1: Find nearest lower cube

$4^3 = 4\times4\times4 = 64$

Step2: Find nearest higher cube

$5^3 = 5\times5\times5 = 125$

Step3: Compare cube to 74

Since $64 < 74 < 125$, take cube roots: $\sqrt[3]{64} < \sqrt[3]{74} < \sqrt[3]{125}$

Step4: Simplify cube roots

$\sqrt[3]{64}=4$, $\sqrt[3]{125}=5$

Answer:

$4 < \sqrt[3]{74} < 5$