Question

simplify.
$5\sqrt{343}$

Explanation:

Step1: Factorize 343

We know that \(343 = 7\times7\times7=7^{3}\), so \(\sqrt{343}=\sqrt{7^{3}}\).

Step2: Simplify the square - root

Using the property of square - roots \(\sqrt{a^{m}}=a^{\frac{m}{2}}\) (for \(a\geq0\)), when \(a = 7\) and \(m = 3\), we have \(\sqrt{7^{3}}=7^{\frac{3}{2}}=7\times\sqrt{7}\) (because \(7^{\frac{3}{2}}=7^{1 + \frac{1}{2}}=7\times7^{\frac{1}{2}}=7\sqrt{7}\)).

Step3: Multiply by 5

Now, we have \(5\sqrt{343}=5\times7\sqrt{7}\).
Calculating \(5\times7 = 35\), so \(5\sqrt{343}=35\sqrt{7}\).

Answer:

\(35\sqrt{7}\)