solubility 3rd root

[recyrb]

Advertisement - Members don't see this ad

Hey guys, I was wondering if you could help me with taking the 3rd root or 4 root of a number, particularly for solubility products, etc..

2 x 10^-6 = 4x^3

2 x 10^-6 = 27x^4

I understand the square root, because the scientific exponent is just 1/2 of the initial so what about these? thanks

 

[wall1two]

Hey guys, I was wondering if you could help me with taking the 3rd root or 4 root of a number, particularly for solubility products, etc..

2 x 10^-6 = 4x^3

2 x 10^-6 = 27x^4

I understand the square root, because the scientific exponent is just 1/2 of the initial so what about these? thanks

It is all about manipulating the number so the exponent and base of the ksp are easier to deal with, i would first divide the first one by 4 on both sides. giving .5*10^-6 . then i would turn the ksp into 500*10^-9 by moving the decimal over 3 places. 9 is easily divisible by 3 (the exponents) = -3 and the third root of 500 is far less tricky than the third root of .5. 5*5*5 = 175 and 10*10*10= 1000, so pick something in the middle, but do to the nature of exponent, something closer to 10, about 7-8.

giving your solubility product of ~7.5 * 10^ -3


for the second one start with 200*10^-8= 27x^4 if your round 27 down to 25 the problem is a breeze, then at the end realize the answer you found will be slightly higher than the actual (you divided by a rounded down number) .

 

[recyrb]

thanks wall