Question

Use the expansion of (4 + x)^3 to find the exact value of (4.02)3

Answer 1

$\text{we know,}$
$(a + x)^n = a + nx , \text{where a is very very greater than x}$
here given, (4.02)³
= (4 + 0.02)³
you can see that , 4 >>0.02
so, we can use binomial expansion.
so, (4.02)³ = 4 + 3 × 0.02
= 4 + 0.06 = 4.06

hence answer is 4.06