Absolutely, let's break down the expression step-by-step:
We want to find the square root of the fraction:
[tex]\[
\sqrt{\frac{(0.000027 \times 10^{16})(0.324 \times 10^{-8})}{(0.0081 \times 10^{-5})(30000 \times 10^{-10})}}
\][/tex]
To do this, we'll:
1. Calculate the product in the numerator.
2. Calculate the product in the denominator.
3. Divide the numerator by the denominator.
4. Find the square root of the result.
### Step 1: Calculate the Products in the Numerator
The numerator consists of the terms: [tex]\(0.000027 \times 10^{16}\)[/tex] and [tex]\(0.324 \times 10^{-8}\)[/tex].
- For [tex]\(0.000027 \times 10^{16}\)[/tex]:
- [tex]\(0.000027 \times 10^{16} = 270000000000.0\)[/tex]
- For [tex]\(0.324 \times 10^{-8}\)[/tex]:
- [tex]\(0.324 \times 10^{-8} = 3.24 \times 10^{-9}\)[/tex]
Now, multiply these two results together:
- [tex]\(270000000000.0 \times 3.24 \times 10^{-9} = 874.8\)[/tex]
### Step 2: Calculate the Products in the Denominator
The denominator consists of the terms: [tex]\(0.0081 \times 10^{-5}\)[/tex] and [tex]\(30000 \times 10^{-10}\)[/tex].
- For [tex]\(0.0081 \times 10^{-5}\)[/tex]:
- [tex]\(0.0081 \times 10^{-5} = 8.1 \times 10^{-8}\)[/tex]
- For [tex]\(30000 \times 10^{-10}\)[/tex]:
- [tex]\(30000 \times 10^{-10} = 3 \times 10^{-6}\)[/tex]
Now, multiply these two results together:
- [tex]\(8.1 \times 10^{-8} \times 3 \times 10^{-6} = 2.43 \times 10^{-13}\)[/tex]
### Step 3: Divide the Numerator by the Denominator
Now, we have:
- Numerator: [tex]\( 874.8 \)[/tex]
- Denominator: [tex]\( 2.43 \times 10^{-13} \)[/tex]
Dividing these two results gives us:
[tex]\[
\frac{874.8}{2.43 \times 10^{-13}} \approx 3.6 \times 10^{14}
\][/tex]
### Step 4: Find the Square Root of the Result
Finally, we find the square root of [tex]\( 3.6 \times 10^{14} \)[/tex]:
[tex]\[
\sqrt{60000000000} = 60000000.0
\][/tex]
Thus, the solution to the expression is [tex]\(60,000,000.0\)[/tex].
