Question

select true or false to the following statement:
the radical expressions \\(\sqrt{2}\\) and \\(\sqrt{12}\\) can be combined after simplifying, to become one radical expression through addition or subtraction.

Explanation:

Step1: Simplify \(\sqrt{12}\)

We know that \(12 = 4\times3\), and \(\sqrt{ab}=\sqrt{a}\times\sqrt{b}\) (for \(a\geq0,b\geq0\)). So \(\sqrt{12}=\sqrt{4\times3}=\sqrt{4}\times\sqrt{3}=2\sqrt{3}\).

Step2: Analyze \(\sqrt{2}\) and \(2\sqrt{3}\)

Radical expressions can be combined (through addition or subtraction) only if they are like radicals, i.e., they have the same radicand (the number inside the square root). Here, \(\sqrt{2}\) has a radicand of \(2\) and \(2\sqrt{3}\) has a radicand of \(3\). Since the radicands are different, they are not like radicals and cannot be combined into one radical expression through addition or subtraction.

Answer:

False