simplify.\n$5\\sqrt{147}$

Explanation:

Step 1: Factor 147 into perfect square and other factor

We know that (147 = 49\times3), where (49) is a perfect square ((49 = 7^2)). So we can rewrite (\sqrt{147}) as (\sqrt{49\times3}).

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

Applying the property, (\sqrt{49\times3}=\sqrt{49}\times\sqrt{3}). Since (\sqrt{49} = 7), this simplifies to (7\sqrt{3}).

Step 3: Multiply by the coefficient outside the square root

We have (5\sqrt{147}=5\times7\sqrt{3}). Multiplying (5) and (7) gives (35). So (5\sqrt{147}=35\sqrt{3}).

Answer:

(35\sqrt{3})