SOLUTION: Please how to calculate the cubic root of numbers by hand.Please help me with this equation 35=3*(8.5) + (cubic root a + (169)) Please give me a detailed explanation and solu

Algebra ->  Square-cubic-other-roots -> SOLUTION: Please how to calculate the cubic root of numbers by hand.Please help me with this equation 35=3*(8.5) + (cubic root a + (169)) Please give me a detailed explanation and solu      Log On


   

Question 848999: Please how to calculate the cubic root of numbers by hand.Please help me with this equation
35=3*(8.5) + (cubic root a + (169))
Please give me a detailed explanation and solution to this question.
Answer by josgarithmetic(39617) About Me  (Show Source):
You can put this solution on YOUR website!
You are trying to show 35=3%2A%288.5%29%2B%28root%283%2Ca%29%2B169%29 according to what you wrote.

First, isolate the root(3,a).
35=3%288.5%29%2Broot%283%2Ca%29%2B169
root%283%2Ca%29=35-3%288.5%29-169, the parentheses not having any effect.
root%283%2Ca%29=-159.5
This is the same as -root%283%2Ca%29=159.5; and the result would be irrational.

There are methods to do this by hand; or you could do it in in a more simple manner using or starting from known cubes of whole numbers. You could go a bit fancier and use logarithms. No matter how to go through, the result will be an approximation.

5%5E3=125; 6%5E3=216; you would or could test values between 5 and 6, being something near to 5.5.
(You would find that 5.50%5E3=166.375, and 5.4%5E3=157.464; you might then either try linear interpolation, or look for another cubic multiplication between 5.4 and 5.5.)