Question

1. simplify \\(\sqrt{98}\\). express the answer in simplest form. \\(2\sqrt{7}\\) \\(49\sqrt{2}\\) \\(7\sqrt{2}\\) \\(49\\)

Explanation:

Step1: Factor the radicand

We factor 98 into a product of a perfect square and another number. We know that \(98 = 49\times2\), where 49 is a perfect square (\(49 = 7^2\)). So we can rewrite \(\sqrt{98}\) as \(\sqrt{49\times2}\).

Step2: Use the property of square roots

Using the property \(\sqrt{ab}=\sqrt{a}\times\sqrt{b}\) (where \(a\geq0\) and \(b\geq0\)), we can split the square root: \(\sqrt{49\times2}=\sqrt{49}\times\sqrt{2}\).

Step3: Simplify \(\sqrt{49}\)

Since \(7^2 = 49\), \(\sqrt{49}=7\). So substituting back, we get \(7\times\sqrt{2}=7\sqrt{2}\).

Answer:

\(7\sqrt{2}\) (corresponding to the option \(7\sqrt{2}\))