Let's solve the expression step-by-step.
### Step 1: Simplify the expression inside the square root.
We start with the given expression:
[tex]\[ 1.28 \times \sqrt{7 \times 15^2 \times 100^2 \times 3^2} \][/tex]
First, we simplify the powers:
[tex]\[ 15^2 = 225 \][/tex]
[tex]\[ 100^2 = 10000 \][/tex]
[tex]\[ 3^2 = 9 \][/tex]
### Step 2: Substitute the simplified values back into the expression.
Now the expression inside the square root becomes:
[tex]\[ 7 \times 225 \times 10000 \times 9 \][/tex]
### Step 3: Calculate the product inside the square root.
We multiply these values step by step:
[tex]\[ 7 \times 225 = 1575 \][/tex]
[tex]\[ 1575 \times 10000 = 15750000 \][/tex]
[tex]\[ 15750000 \times 9 = 141750000 \][/tex]
Thus, the value inside the square root is:
[tex]\[ 141750000 \][/tex]
### Step 4: Take the square root of the calculated value.
Next, we find the square root:
[tex]\[ \sqrt{141750000} \approx 11905.097304475033 \][/tex]
### Step 5: Multiply by 1.28.
Finally, we multiply the square root by the given coefficient, 1.28:
[tex]\[ 1.28 \times 11905.097304475033 \approx 15239.527551732 \][/tex]
### Conclusion
Therefore, the value inside the square root is:
[tex]\[ 141750000 \][/tex]
And the final value of the expression is approximately:
[tex]\[ 15239.527551732 \][/tex]
This is the detailed step-by-step solution of the given problem.
