Question

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

Explanation:

Step1: Factorize 343

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

Step2: Use square - root property

Using the property of square roots \( \sqrt{ab}=\sqrt{a}\times\sqrt{b} \) (where \( a = 49 \) and \( b = 7 \) and \( a\geq0,b\geq0 \)), we have \( \sqrt{49\times7}=\sqrt{49}\times\sqrt{7} \).
Since \( \sqrt{49} = 7 \), then \( \sqrt{49}\times\sqrt{7}=7\sqrt{7} \).

Answer:

\( 7\sqrt{7} \) (the option with the label \( 7\sqrt{7} \))