simplify.\n$7\\sqrt{20}$

Explanation:

Step1: Factor the radicand

We know that (20 = 4\times5), and (4) is a perfect square. So we can rewrite (\sqrt{20}) as (\sqrt{4\times5}). (7\sqrt{20}=7\sqrt{4\times5})

Step2: Use the property of square roots

The property (\sqrt{ab}=\sqrt{a}\times\sqrt{b}) (where (a\geq0), (b\geq0)) allows us to split the square root. So (\sqrt{4\times5}=\sqrt{4}\times\sqrt{5}). Since (\sqrt{4} = 2), we have: (7\sqrt{4\times5}=7\times\sqrt{4}\times\sqrt{5}=7\times2\times\sqrt{5})

Step3: Multiply the coefficients

Multiply (7) and (2) to get (14). So the simplified form is: (14\sqrt{5})

Answer:

(14\sqrt{5})