Question

How can I simplify these?

Answer 1

Answer:

$\large\boxed{343=7\sqrt7}\\\boxed{10\sqrt{96}=40\sqrt6}$

Step-by-step explanation:

$343=7^3=7^2\cdot7\\\\\sqrt{343}=\sqrt{7^2\cdot7}\qquad\text{use}\ \sqrt{ab}=\sqrt{a}\cdot\sqrt{b}\\\\=\sqrt{7^2}\cdot\sqrt7\qquad\text{use}\ \sqrt{a^2}=a\ \text{for}\ a\geq0\\\\=7\sqrt7\\=====================\\\\96=16\cdot6\\\\10\sqrt{96}=10\sqrt{16\cdot6}=10\sqrt{16}\cdot\sqrt6=(10)(4)\sqrt6=40\sqrt6$