Question

simplify.
\sqrt{5c} \cdot \sqrt{5c}
assume that the variable represents a positive real number.

Explanation:

Step1: Recall the property of square roots

The product of two square roots \(\sqrt{a} \cdot \sqrt{b}=\sqrt{ab}\) (for \(a\geq0,b\geq0\)). Here, \(a = 5c\) and \(b = 5c\), so \(\sqrt{5c}\cdot\sqrt{5c}=\sqrt{(5c)\cdot(5c)}\).

Step2: Simplify the radicand

\((5c)\cdot(5c)=(5c)^2\), so we have \(\sqrt{(5c)^2}\).

Step3: Evaluate the square root

Since the variable \(c\) represents a positive real number, \(5c\) is positive. The square root of a square of a positive number \(x\) is \(x\), so \(\sqrt{(5c)^2}=5c\).

Answer:

\(5c\)