Complete the expression subtracting the radicals.

Question

?sqrt?-?sqrt?=?sqrt?
not all ?s are the same. find the value of all ?s. each sqrt is comprised of 2 different integers(ex. 3sqrt5)

Answer 1

To complete the expression and solve for the radical equation in the form:

\[ \sqrt{a} - \sqrt{b} = \sqrt{c} \]

Let's assign integers to \(a\), \(b\), and \(c\). Not all values need to be the same, and the radicals should be composed of integers where necessary.

Let's take a specific example:

1. Let's say \( \sqrt{8} - \sqrt{2} = ?\)
2. We know: \[ \sqrt{8} = 2\sqrt{2} \] Therefore: \[ 2\sqrt{2} - \sqrt{2} = (2 - 1)\sqrt{2} = 1\sqrt{2} \]

From the above, we can substitute \(c\): \[ c = 2 \]

Thus, we have:

\[ \sqrt{8} - \sqrt{2} = \sqrt{2} \]

In our example, the values are:

• \( a = 8 \)
• \( b = 2 \)
• \( c = 2 \)

You can choose different values for \(a\), \(b\), but you would still arrive at the conclusion that when subtracting radicals, they need to be similar to simplify directly.