Question

simplify \\(\sqrt{75}\\) ?

Explanation:

Step1: Factor 75 into primes

We know that \( 75 = 25\times3 \), and \( 25 = 5^2 \). So, \( 75 = 5^2\times3 \).

Step2: Apply square - root property

Using the property of square roots \(\sqrt{ab}=\sqrt{a}\times\sqrt{b}\) (where \(a = 5^2\) and \(b = 3\)) and \(\sqrt{a^2}=a\) (for \(a\geq0\)), we have \(\sqrt{75}=\sqrt{5^2\times3}=\sqrt{5^2}\times\sqrt{3}\).
Since \(\sqrt{5^2} = 5\), then \(\sqrt{75}=5\sqrt{3}\).

Answer:

\(5\sqrt{3}\)