Question
Evaluate the following: $(9.9)^3$
✓
Answer
We know that $(a - b)^3 = a^3 - b^3 - 3ab(a - b)$
$\Rightarrow (9.9)^3$ can be written as $(10 - 0.1)^3$
Here$, a = 10$ and $b = 0.1$
$(9.9)^3 = (10 - 0.1)^3$
$= (10)^3 - (0.1)^3 - 3(10)(0.1)(10 - 0.1)$
$= 1000 - 0.001 - (3 \times 9.9)$
$= 1000 - 0.001 - 29.7$
$= 1000 - 29.701$
$= 970.299$
The value of $(9.9)^3 = 970.299$
$\Rightarrow (9.9)^3$ can be written as $(10 - 0.1)^3$
Here$, a = 10$ and $b = 0.1$
$(9.9)^3 = (10 - 0.1)^3$
$= (10)^3 - (0.1)^3 - 3(10)(0.1)(10 - 0.1)$
$= 1000 - 0.001 - (3 \times 9.9)$
$= 1000 - 0.001 - 29.7$
$= 1000 - 29.701$
$= 970.299$
The value of $(9.9)^3 = 970.299$
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