Of course, let's solve the expression step-by-step in a clear and detailed manner:
Given expression:
[tex]\[ \frac{4 \sqrt{1250}}{4 \sqrt{2}} \][/tex]
Step 1: Simplify the fraction.
Since the numerator and the denominator both have a common factor of [tex]\(4\)[/tex], we can cancel those out:
[tex]\[ \frac{4 \sqrt{1250}}{4 \sqrt{2}} = \frac{\sqrt{1250}}{\sqrt{2}} \][/tex]
Step 2: Simplify the square roots.
To make this expression simpler, we can combine the square roots in the numerator and denominator as a single square root:
[tex]\[ \frac{\sqrt{1250}}{\sqrt{2}} = \sqrt{\frac{1250}{2}} \][/tex]
Step 3: Divide the numbers under the square root.
[tex]\[ \frac{1250}{2} = 625 \][/tex]
So the expression simplifies to:
[tex]\[ \sqrt{625} \][/tex]
Step 4: Find the square root of the result.
[tex]\[ \sqrt{625} = 25 \][/tex]
Thus, the value of the given expression is:
[tex]\[ 25 \][/tex]
So, [tex]\(\frac{4 \sqrt{1250}}{4 \sqrt{2}} = 25\)[/tex].
