Question

question 2 of 5
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

First, we factorize 343. We know that \( 343 = 49\times7 \), and \( 49 = 7^2 \). So, \( 343 = 7^2\times7 \).

Step2: Simplify the square root

Using the property of square roots \( \sqrt{ab}=\sqrt{a}\times\sqrt{b} \) (where \( a\geq0 \) and \( b\geq0 \)), we can rewrite \( \sqrt{343} \) as \( \sqrt{7^2\times7} \). Then, by the property \( \sqrt{ab}=\sqrt{a}\times\sqrt{b} \), this becomes \( \sqrt{7^2}\times\sqrt{7} \). Since \( \sqrt{7^2} = 7 \), we have \( 7\sqrt{7} \).

Now let's check the other options:

• Option \( 7\sqrt{49} \): \( \sqrt{49}=7 \), so \( 7\sqrt{49}=7\times7 = 49 \), which is not equal to \( \sqrt{343} \) (since \( \sqrt{343}\approx18.52 \) and \( 49

eq18.52 \)).

• Option \( 49\sqrt{7} \): \( 49\sqrt{7}\approx49\times2.6458\approx129.64 \), which is not equal to \( \sqrt{343} \).
• Option \( 7 \): \( 7^2 = 49

eq343 \), so this is incorrect.

Answer:

D. \( 7\sqrt{7} \) (assuming the options are labeled A, B, C, D with D being \( 7\sqrt{7} \))