Question

multiply. write your answer in simplest form.\\(sqrt{343} cdot sqrt{5}\\)

Explanation:

Step1: Use the property of square roots $\sqrt{a}\cdot\sqrt{b}=\sqrt{ab}$

$\sqrt{343}\cdot\sqrt{5}=\sqrt{343\times5}$

Step2: Factorize 343

We know that $343 = 7^3=7^2\times7$, so $343\times5 = 7^2\times7\times5=7^2\times35$

Step3: Simplify the square root

$\sqrt{7^2\times35}=\sqrt{7^2}\times\sqrt{35}=7\sqrt{35}$

Answer:

$7\sqrt{35}$