AI Tutor
Imagine building a storage crate shaped like a perfect cube that must hold exactly 50 ft350\text{ ft}^3 of gear. To build the wooden frame, what should the length of each edge be?
Finding that edge means finding a number that multiplies by itself three times to equal 5050 — an operation known as finding a cube root, written as 503\sqrt[3]{50}.
Can we just divide 5050 by 33? Let's look at why cube roots don't work that way.

What Makes a Cube Root?

A perfect cube is an integer formed by multiplying three identical integers together, like 3×3×3=273 \times 3 \times 3 = 27.
A cube root does the exact reverse: if a3=ba^3 = b, then b3=a\sqrt[3]{b} = a.
Since 5050 is not on our list of perfect cubes, its cube root is an irrational number that continues forever without repeating. How do we pinpoint its whole-number neighbors?

Trapping the Root Between Integers

To bracket an unknown cube root, find the two closest consecutive perfect cubes that sandwich your target number.
Because 27<50<6427 < 50 < 64, taking the cube root across all three gives 273<503<643\sqrt[3]{27} < \sqrt[3]{50} < \sqrt[3]{64}, meaning 3<503<43 < \sqrt[3]{50} < 4.