Question

evaluate. write your answer as a decimal or whole number.
$(8.1)^3 = \square$

Explanation:

Step1: Recall the formula for cube of a number

The cube of a number \(a\) is given by \(a^3=a\times a\times a\). So for \(a = 8.1\), we need to calculate \(8.1\times8.1\times8.1\).

Step2: Calculate \(8.1\times8.1\)

\(8.1\times8.1=(8 + 0.1)\times(8+0.1)\) using the formula \((a + b)^2=a^{2}+2ab + b^{2}\), where \(a = 8\) and \(b=0.1\).
\(a^{2}=8^{2}=64\), \(2ab = 2\times8\times0.1 = 1.6\), \(b^{2}=0.1^{2}=0.01\). So \((8 + 0.1)^{2}=64+1.6 + 0.01=65.61\).

Step3: Multiply the result by 8.1

Now we multiply \(65.61\) by \(8.1\). \(65.61\times8.1 = 65.61\times(8+0.1)=65.61\times8+65.61\times0.1\).
\(65.61\times8 = 524.88\) and \(65.61\times0.1=6.561\).
Adding these two results: \(524.88+6.561 = 531.441\).

Answer:

\(531.441\)