# What is the cube root of 88?

Mar 6, 2018

$\sqrt[3]{88} = 2 \sqrt[3]{11}$ or decimal approximation to 25 decimal places that is 4.4479601811386310423307268

#### Explanation:

find a factor that is a cube number

$\sqrt[3]{8 \cdot 11}$

seperate the multiples using the radical law $\sqrt[n]{x y} = \sqrt[n]{x} \cdot \sqrt[n]{y}$

$\sqrt[3]{8} \cdot \sqrt[3]{11}$

The cube root of 8 is 2

$2 \cdot \sqrt[3]{11}$

$2 \sqrt[3]{11}$

Mar 6, 2018

See a see a solution process below

#### Explanation:

We can rewrite this expression as:

$\sqrt[3]{88} \implies \sqrt[3]{8 \cdot 11}$

We can then use this rule for radicals to simplify the expression:

$\sqrt[n]{\textcolor{red}{a} \cdot \textcolor{b l u e}{b}} = \sqrt[n]{\textcolor{red}{a}} \cdot \sqrt[n]{\textcolor{b l u e}{b}}$

$\sqrt[3]{\textcolor{red}{8} \cdot \textcolor{b l u e}{11}} \implies \sqrt[3]{\textcolor{red}{8}} \cdot \sqrt[3]{\textcolor{b l u e}{11}} \implies 2 \sqrt[3]{11}$

If you need an exact number: $\sqrt[3]{88} \implies 4.448$ rounded to the nearest thousandth.