simplify.\n$8\\sqrt{343}$

Explanation:

Step1: Factorize 343

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

Step2: Simplify the square root

Using the property (\sqrt{ab}=\sqrt{a}\times\sqrt{b}) (for (a\geq0,b\geq0)), we have (\sqrt{7^2\times7}=\sqrt{7^2}\times\sqrt{7}=7\sqrt{7}).

Step3: Multiply with the coefficient

Now, multiply this with the coefficient 8. So, (8\sqrt{343}=8\times7\sqrt{7}=56\sqrt{7}).

Answer:

(56\sqrt{7})