Question

simplify.
\sqrt{245}

Explanation:

Step 1: Factor the number inside the square root

We need to factor 245 into a product of a perfect square and another number. We know that \(245 = 49\times5\), where 49 is a perfect square (\(7^2\)). So we can rewrite \(\sqrt{245}\) as \(\sqrt{49\times5}\).

Step 2: Use the property of square roots \(\sqrt{ab}=\sqrt{a}\times\sqrt{b}\) (for \(a\geq0,b\geq0\))

Applying the property \(\sqrt{ab}=\sqrt{a}\times\sqrt{b}\) to \(\sqrt{49\times5}\), we get \(\sqrt{49}\times\sqrt{5}\). Since \(\sqrt{49} = 7\) (because \(7^2 = 49\)), the expression simplifies to \(7\sqrt{5}\).

Answer:

\(7\sqrt{5}\)