Find the cube of $2.1$

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Solution

The given number ${2.1}^{3}$ can be rewritten as $(2 + 0.1)^{3}$

We know that the identity is $(a + b)^{3} = a^{3} + b^{3} + 3 a^{2} b + 3 a b^{2}$

Therefore,

${(2 + 0.1)}^{3} = (2)^{3} + {(0.1)}^{3} + (3 \times (2)^{2} \times 0.1) + (3 \times 2 \times {(0.1)}^{2}) = 8 + 0.001 + (0.3 \times 4) + (6 \times 0.01)$
$= 8 + 0.001 + 1.2 + 0.06 = 9.261$

Hence, ${2.1}^{3} = 9.261$ .

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