# What is square root of 0.003 + cube root of 0.000125?

Sep 21, 2015

$0.053$

#### Explanation:

$0.000125 = 0.05 \cdot 0.0025 = 0.05 \cdot 0.05 \cdot 0.05 = {0.05}^{3}$
$\sqrt[3]{0.000125} = {\sqrt[3]{0.05}}^{3} = 0.05$
$\sqrt[3]{0.000125} + 0.003 = 0.05 + 0.003 = 0.053$

Sep 21, 2015

$0.1 \sqrt{0.3} + 0.05 \approx 0.10477225575$

#### Explanation:

$\sqrt{0.003} + \sqrt[3]{0.000125}$

$= \sqrt{0.003} + \sqrt[3]{125 \cdot 0.000001}$

$= \sqrt{0.003} + \sqrt[3]{{5}^{3} \cdot {0.01}^{3}}$

$= \sqrt{0.003} + \left(5\right) \left(0.01\right)$

$= \sqrt{0.003} + 0.05$

$= \sqrt{3 \cdot 0.001} + 0.05$

$= \sqrt{3 \cdot {0.1}^{3}} + 0.05$

$= \textcolor{red}{0.1 \sqrt{0.3} + 0.05}$

You won't be able to simplify that any further since there are no more perfect square factors of $0.3$. However, if you are using a calculator, you can easily solve this problem. You should get approximately $0.10477225575$.