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 \(a\geq0\) and \(m\) is an integer), we have \(\sqrt{7^{3}} = 7^{\frac{3}{2}}=7^{1+\frac{1}{2}} = 7\times\sqrt{7}\) (since \(a^{m + n}=a^{m}\times a^{n}\) and \(a^{\frac{1}{2}}=\sqrt{a}\)).

Step3: Multiply by 5

Now, \(5\sqrt{343}=5\times7\sqrt{7}=35\sqrt{7}\).

Answer:

\(35\sqrt{7}\)