Question

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

Answer 1

`0.053`

Explanation:

`0.000125=0.05*0.0025=0.05*0.05*0.05=0.05^3`
`root(3)0.000125=root(3)0.05^3=0.05`
`root(3)0.000125+0.003=0.05+0.003=0.053`

Answer 2

`0.1sqrt0.3+0.05~~0.10477225575`

Explanation:

`sqrt0.003+root(3)0.000125`

`=sqrt0.003+root(3)(125*0.000001)`

`=sqrt0.003+root(3)(5^3*0.01^3)`

`=sqrt0.003+(5)(0.01)`

`=sqrt0.003+0.05`

`=sqrt(3*0.001)+0.05`

`=sqrt(3*0.1^3)+0.05`

`=color(red)(0.1sqrt0.3+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`.