What is the cube root of 297?

Sep 21, 2015

$\sqrt[3]{297} = 3 \sqrt[3]{11}$

Explanation:

$\sqrt[3]{297}$

Factor it out, sice $2 + 9 + 7 = 18$ we know 297 is divisible by 9.

$\sqrt[3]{297} = \sqrt[3]{33 \cdot 9}$

Since $3 + 3 = 6$ we know 33 is divisible by 3

$\sqrt[3]{33 \cdot 9} = \sqrt[3]{11 \cdot 3 \cdot 9}$

11 is a prime number so there's no more factoring do. We know that $9 = {3}^{2}$, so we can rewrite $3 \cdot 9 = 3 \cdot {3}^{2} = {3}^{3}$

$\sqrt[3]{33 \cdot 9} = \sqrt[3]{11 \cdot {3}^{3}}$

The ${3}^{3}$ can go out of the root, so

$\sqrt[3]{297} = 3 \sqrt[3]{11}$