# How do you find the cube root of 0.000343?

Jun 26, 2016

$\sqrt[3]{0.000343} = 0.07$

#### Explanation:

Note that $0.000343 = 343 \cdot {10}^{- 6}$ and $343 = {7}^{3}$

So:

$\sqrt[3]{0.000343} = \sqrt[3]{343 \cdot {10}^{- 6}} = \sqrt[3]{343} \cdot \sqrt[3]{{10}^{- 6}}$

$= \sqrt[3]{{7}^{3}} \cdot {10}^{- 2} = 7 \cdot {10}^{- 2} = 0.07$

Jun 26, 2016

$0.07$

#### Explanation:

Group the decimals in three's from the decimal.
Each group must have one number.

$\sqrt[3]{\text{0.000 343}}$

$\sqrt[3]{0.000} = 0$

$\sqrt[3]{343} = 7$

$\sqrt[3]{\text{0.000 343}} = 0.07$

Check: 2 decimal places cubed will give 6 decimal places.