Question

determine whether the expression is in simplest form.\\(sqrt{18}\\)\
the expression \\(\quad\\) in its simplest form.\
if the expression is not in simplest form, explain why.

Explanation:

Step1: Factor the radicand

We factor 18 into a product of a perfect square and another number. We know that \(18 = 9\times2\), where 9 is a perfect square (\(9 = 3^2\)). So, \(\sqrt{18}=\sqrt{9\times2}\).

Step2: Use the property of square roots

Using the property \(\sqrt{ab}=\sqrt{a}\times\sqrt{b}\) (for \(a\geq0,b\geq0\)), we can rewrite \(\sqrt{9\times2}\) as \(\sqrt{9}\times\sqrt{2}\).

Step3: Simplify the perfect square root

Since \(\sqrt{9} = 3\), we have \(\sqrt{18}=3\sqrt{2}\). So, the original expression \(\sqrt{18}\) is not in simplest form because the radicand 18 has a perfect - square factor (9) other than 1.

Answer:

The expression is not in its simplest form. Because the radicand 18 can be factored as \(9\times2\), where 9 is a perfect square (\(9 = 3^2\)), and using the square - root property \(\sqrt{ab}=\sqrt{a}\times\sqrt{b}\) (\(a\geq0,b\geq0\)), \(\sqrt{18}\) can be simplified to \(3\sqrt{2}\).