Certainly! Let's work with the expression in the form \( a\sqrt{b} - c\sqrt{d} = e\sqrt{f} \). Here's an example to illustrate the subtraction of radicals:
\[ 3\sqrt{8} - 2\sqrt{2} = e\sqrt{f} \]
First, we simplify \(3\sqrt{8}\):
\[ \sqrt{8} = \sqrt{4 \cdot 2} = \sqrt{4} \cdot \sqrt{2} = 2\sqrt{2} \]
Thus,
\[ 3\sqrt{8} = 3 \cdot 2\sqrt{2} = 6\sqrt{2} \]
Now, we can rewrite the expression:
\[ 6\sqrt{2} - 2\sqrt{2} = (6 - 2)\sqrt{2} = 4\sqrt{2} \]
So we have:
\[ 3\sqrt{8} - 2\sqrt{2} = 4\sqrt{2} \]
Thus, assigning the values gives:
- \( a = 3 \)
- \( b = 8 \)
- \( c = 2 \)
- \( d = 2 \)
- \( e = 4 \)
- \( f = 2 \)
So the original equation works out as:
\[ 3\sqrt{8} - 2\sqrt{2} = 4\sqrt{2} \]
Feel free to ask if you'd like to see another example!