Sure, let's simplify the given radical expression step by step.
The given expression to simplify is:
[tex]\[
\sqrt{8} \cdot \sqrt{18} \cdot 5 \cdot \sqrt{4}
\][/tex]
### Step 1: Break down each square root term
First, let's simplify the square roots individually.
- [tex]\(\sqrt{8}\)[/tex]:
[tex]\[
\sqrt{8} = \sqrt{4 \cdot 2} = \sqrt{4} \cdot \sqrt{2} = 2\sqrt{2}
\][/tex]
- [tex]\(\sqrt{18}\)[/tex]:
[tex]\[
\sqrt{18} = \sqrt{9 \cdot 2} = \sqrt{9} \cdot \sqrt{2} = 3\sqrt{2}
\][/tex]
- [tex]\(\sqrt{4}\)[/tex]:
[tex]\[
\sqrt{4} = 2
\][/tex]
### Step 2: Substitute the simplified values back into the original expression
Replace the simplified square root values:
[tex]\[
\sqrt{8} \cdot \sqrt{18} \cdot 5 \cdot \sqrt{4} = (2\sqrt{2}) \cdot (3\sqrt{2}) \cdot 5 \cdot 2
\][/tex]
### Step 3: Multiply the coefficients
Now, combine the coefficients (constants) together:
[tex]\[
2 \cdot 3 \cdot 5 \cdot 2 = 60
\][/tex]
### Step 4: Multiply the square root terms
Now, multiply the radical parts:
[tex]\[
\sqrt{2} \cdot \sqrt{2} = \sqrt{2 \cdot 2} = \sqrt{4} = 2
\][/tex]
### Step 5: Combine the results
Multiplying the coefficient (60) by the result of the radical parts (2):
[tex]\[
60 \cdot 2 = 120
\][/tex]
### Final Answer
The simplified radical expression is:
[tex]\[
120
\][/tex]
Thus, the exact value of the given radical expression is [tex]\(120\)[/tex].
