Ksp Math help..

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7+ Year Member
Oct 30, 2013
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I understand Ksp and formula set up and everything but I am having trouble with the math. Specially taking the sqrt of the numbers.

for example lets say Ksp = 3.3 x 10^-9= [x][x]

3.3 x 10^-9 =x^2

sqrt(3.3 x 10^-9) = x

My question is what is the fastest way to do the math here. From my understand the sqrt of 10^-9 = 10^(-9/2). What is the fastest way to take the square root of 3.3 without the guess and check and obviously without the calculator.

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First, always adjust the scientific notation to make the exponent an even number. It'll make your life worlds easier.

3.3 x 10^-9 = 33 x 10^-10 = x^2

Then you can just cut the exponent in half. Honestly the coefficient matters MUCH less when distinguishing between answer choices on many MCAT problems. Often getting anywhere close is good enough.

So here, you'd say "okay 33 is between 25 and 36, so my coefficient is between 5 and 6 when I root it."

x is roughly 5.7 x 10^-5
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Thank you very much. I knew this process haha but I was thinking too hard but thank you very much for reminding me and for the help kind sir/madam.