Sure, let's break down the expression [tex]\(3\sqrt{496^3}d\)[/tex] step by step.
1. Simplify the inner power:
First, we need to calculate [tex]\(496^3\)[/tex].
[tex]\[
496^3 = 496 \times 496 \times 496 = 121,287,296 \times 496 = 60,211,306,496
\][/tex]
2. Calculate the square root:
Now, we need to take the square root of the result from step 1:
[tex]\[
\sqrt{60,211,306,496}
\][/tex]
3. Simplify with the cube root:
Then, we need to take the cube root of the square root computed in step 2:
[tex]\[
3\sqrt{60,211,306,496}
\][/tex]
To simplify, we know:
[tex]\[
3\sqrt{a^3} = a
\][/tex]
Therefore:
[tex]\[
\sqrt{60,211,306,496} = \sqrt{(496^3)} = 496
\][/tex]
Thus:
[tex]\[
3\sqrt{(60,211,306,496)} = 3 \times 496 = 1488
\][/tex]
4. Incorporate the variable [tex]\(d\)[/tex]:
Finally, we include the variable [tex]\(d\)[/tex]:
[tex]\[
1488d
\][/tex]
So, the simplified form of the original expression is:
[tex]\[
1488d
\][/tex]
