Solving for x...

[cougarblue84]

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Hey everyone,

2.1E-6 = 4x(cubed). It's probably simple math to a lot of you, but I was wondering if someone could quickly show how they'd solve for x? I've always depended on the calculator for these types of problems, and I can find square roots without a calculator but what about cubed roots? Thanks for any help!

 

[Shjfr]

Since the DAT is multiple choice I would just plug in X's until I got the right answer (X's that are given as answers of course 😛).

But I'm suuuure there is a better way to do this 🙂

 

[cougarblue84]

That would actually work, as long as there was enough time. Would anyone happen to know an easier way?

 

[mddang]

That would actually work, as long as there was enough time. Would anyone happen to know an easier way?

Wait.. is it 4x^3 or (4x)^3??

I'm going to assume it's 4x^3..



2.1E-6 = 4x^3
21E-7 = 4x^3
do a little rounding and divide both sides by 4..

5E-7 = x^3

Then I will go ahead and make the E-7 easier to take the cube root of by making it E-9
500E-9 = x^3

Now it's cube root time..

The cube root of 500 is less than 10 but more than 5. By simple (but quickly) guess and check, you can find that the cube root of 500 is closest to 8.The cube root of E-9 is E-3.

x = ~8E-3

 

[Streetwolf]

Wait.. is it 4x^3 or (4x)^3??

I'm going to assume it's 4x^3..



2.1E-6 = 4x^3
21E-7 = 4x^3
do a little rounding and divide both sides by 4..

5E-7 = x^3

Then I will go ahead and make the E-7 easier to take the cube root of by making it E-9
500E-9 = x^3

Now it's cube root time..

The cube root of 500 is less than 10 but more than 5. By simple (but quickly) guess and check, you can find that the cube root of 500 is closest to 8.The cube root of E-9 is E-3.

x = ~8E-3

Probably the best way, at least that I can think of at the moment. To make it a bit better I would give the exact quotient of 21/4 = 5.25. Then you'd get 525 * 10^-9. Since 8^3 = 512, you know it is just OVER 8 * 10^-3.