Question

Could you do an expression subtracting radicals using this equation?

?sqrt(?) - ?sqrt(?) = ? sqrt (?)

Answer 1

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!