Answer
$2\sqrt2$.
Work Step by Step
Let the irrational number be $a$.
We can write.
$\Rightarrow a-(2\sqrt{18}-\sqrt{50})=\sqrt2$
Factor the radicands using the greatest perfect square factors inside the parentheses.
$\Rightarrow a-(2\sqrt{2\cdot 3^2}-\sqrt{2\cdot 5^2})=\sqrt2$
Simplify.
$\Rightarrow a-(2\cdot 3\sqrt{2}-5\sqrt{2})=\sqrt2$
$\Rightarrow a-(6\sqrt{2}-5\sqrt{2})=\sqrt2$
Apply the distributive property.
$\Rightarrow a-(6-5)\sqrt{2}=\sqrt2$
Simplify.
$\Rightarrow a-(1)\sqrt{2}=\sqrt2$
Clear the parentheses.
$\Rightarrow a-\sqrt{2}=\sqrt2$
Add $\sqrt 2$ to both sides.
$\Rightarrow a-\sqrt{2}+\sqrt{2}=\sqrt2+\sqrt{2}$
Simplify.
$\Rightarrow a=2\sqrt2$
Hence, the number is $2\sqrt2$.
