Square/Cube roots and Scientific Notation

[mitchlucker]

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Hi, saw a thread 7 years ago for this but it didn't help me out much.

Can anyone tell me an easy way to estimate large/very small square and cube roots?

I get tripped up on problems like solubility when solving for X and I have things like 4.4x10^-14 = 4X^3.

 

[Long Way to Go]

Hi, saw a thread 7 years ago for this but it didn't help me out much.

Can anyone tell me an easy way to estimate large/very small square and cube roots?

I get tripped up on problems like solubility when solving for X and I have things like 4.4x10^-14 = 4X^3.

4.4 * 10^-14 = 4 * x^3
1.1 * 10^-14 = x^3

That's approximately the same as:
10^-14 = x^3

Now, you know that (10^-5)^3 = 10^-15 and (10^-4)^3 = 10^-12. 10^-14 is closer to the former, so you know that x is closer to 10^-5 than 10^-4. 10^-15 is an order of magnitude away from 10^-14, so you want the cube root of 10^1, which is between 2 and 3 (but definitely much closer to 2; I'd estimate around 2.2 or 2.3).
Putting that all together, you get x as about 2.2 * 10^-5.

Does that help? It's kind of complicated, but as you get better, a lot of this stuff becomes quite intuitive.