Question

simplify. assume c is greater than or equ\sqrt{175c^{8}}

Explanation:

Step1: Factor the radicand

We can factor \(175c^8\) as \(25\times7\times c^8\), since \(25\times7 = 175\) and \(c^8=(c^4)^2\). So we have \(\sqrt{25\times7\times c^8}\).

Step2: Use the property of square roots

The property \(\sqrt{ab}=\sqrt{a}\times\sqrt{b}\) (for \(a\geq0,b\geq0\)) allows us to split the square root: \(\sqrt{25}\times\sqrt{7}\times\sqrt{c^8}\).

Step3: Simplify each square root

We know that \(\sqrt{25} = 5\), \(\sqrt{c^8}=c^4\) (because \(c\geq0\), so we don't need to consider the absolute value), and \(\sqrt{7}\) remains as it is. So multiplying these together, we get \(5c^4\sqrt{7}\).

Answer:

\(5c^{4}\sqrt{7}\)