Question

question 3 of 6
select the correct answer.
what is \\(\sqrt{343}\\) in simplest form?
\\(\bigcirc\\) \\(7\sqrt{49}\\)
\\(\bigcirc\\) \\(49\sqrt{7}\\)
\\(\bigcirc\\) \\(7\\)
\\(\bigcirc\\) \\(7\sqrt{7}\\)

Explanation:

Step1: Factorize 343

We know that \(343 = 49\times7\), and \(49 = 7^2\). So, \(\sqrt{343}=\sqrt{7^2\times7}\).

Step2: Use square - root property

According to the property of square roots \(\sqrt{ab}=\sqrt{a}\times\sqrt{b}\) (\(a\geq0,b\geq0\)), we have \(\sqrt{7^2\times7}=\sqrt{7^2}\times\sqrt{7}\).
Since \(\sqrt{7^2} = 7\) (because for any non - negative real number \(x\), \(\sqrt{x^2}=x\) when \(x\geq0\)), then \(\sqrt{7^2}\times\sqrt{7}=7\sqrt{7}\).

Answer:

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