Sure, let's solve the given expression step by step. The expression provided is:
[tex]\[
\frac{80.4^2 \times 78000}{\sqrt{100.5 \times 35.7}}
\][/tex]
We'll break down the solution into parts:
1. Calculate the square of [tex]\(80.4\)[/tex]:
[tex]\[
80.4^2 = 80.4 \times 80.4 = 6464.16
\][/tex]
2. Multiply the square by [tex]\(78000\)[/tex]:
[tex]\[
6464.16 \times 78000 = 504204480.00000006
\][/tex]
So, the numerator of the expression is [tex]\(504204480.00000006\)[/tex].
3. Calculate the product of [tex]\(100.5\)[/tex] and [tex]\(35.7\)[/tex]:
[tex]\[
100.5 \times 35.7 = 3592.85
\][/tex]
4. Take the square root of the product calculated in step 3:
[tex]\[
\sqrt{3592.85} = 59.89866442584509
\][/tex]
So, the denominator of the expression is [tex]\(59.89866442584509\)[/tex].
5. Divide the numerator by the denominator:
[tex]\[
\frac{504204480.00000006}{59.89866442584509} = 8417624.74727977
\][/tex]
So, the final result for the given expression is:
[tex]\[
\boxed{8417624.74727977}
\][/tex]
