Answer to Question #242824 in Algebra for Anand

Question #242824

Find the approximate value of ³√0.99 up to 4 decimal places.


1
Expert's answer
2021-10-14T11:55:37-0400

Let b3=0.99. Also, let us assume that a=1 an ϵ be a small correction factor such that b=a-ϵ.

Now, cubing both sides:

b3=a3-3a2ϵ+3aϵ23

0.99=13ϵ+3ϵ2ϵ30.99=1-3ϵ+3ϵ^2-ϵ^3

Assuming that ϵ3<<ϵ2<<ϵ :

0.99=13ε0.99=1-3\varepsilon

ε=(1099)/3=0.0033\varepsilon=(1-099)/3=0.0033


0.993=10.0033=0.9967\sqrt[3]{0.99}=1-0.0033=0.9967


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