Evaluate the following: (9.9)^3 - Vidyadip

Question

Evaluate the following:
$(9.9)^3$

✓

Answer

We know that $(a-b)^3=a^3-b^3-3 a b(a-b)$
$\Rightarrow(9.9)^3$ can be written as $(10-0.1)^3$
Here, $\mathrm{a}=10$ and $\mathrm{b}=0.1$
$(9.9)^3=(10-0.1)^3$
$=(10)^3-(0.1)^3-3(10)(0.1)(10-0.1)$
$=1000-0.001-(3 \times 9.9)$
$=1000-0.001-29.7$
$=1000-29.701$
$=970.299$
The value of $(9.9)^3=970.299$

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