If y^3 = 8.08, approximate y.
Firstly, recognize that 2^3 is 8, so y must be close to 8.It will be helpful to then write y^3 as y^3= 8 + 0.08We can then factorize out 8.y^3=8(1+0.01)If we try and take the cube root of this expression.y=2(1+0.01)^(1/3)
We recognize this is a binomial expansion, if we label x as 0.01 we can see a more familiar form y=2(1+x)^1/3
Expanding this and truncating the expansion for the first order term, we are left with y = 2 + 2x/3
Substituting in, x=0.01 we get y being roughly equal to 2.01
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