Question

Find the value of \(0.081^3 + 0.009^3 + 0.002187 \times 0.09\).

• A. 0.000729
• B. 0.00729
• C. 0.0000729
• D. 0.0729

Hint:

If an expression matches the form $a^3 + b^3 + 3ab(a+b)$, directly apply: \[ (a+b)^3 \] This saves time and avoids lengthy calculations with decimals.

Answer 1

The Correct Option is A

Concept: The expression is in the form \(a^3 + b^3 + 3ab(a+b)\), which is equal to \((a+b)^3\). Let \(a = 0.081\) and \(b = 0.009\). Note: \(a + b = 0.09\). And \(3ab(a+b) = 3 \times 0.081 \times 0.009 \times 0.09 = 0.002187 \times 0.09\). Simplify the expression.
Value = \((0.081 + 0.009)^3 = (0.09)^3 = 0.000729\).