Question

simplify.
10√363

Explanation:

Step1: Factor the radicand

Factor 363 to find perfect square factors. \(363 = 121\times3\), and \(121 = 11^2\). So, \(\sqrt{363}=\sqrt{121\times3}\).

Step2: Use square root property

Using the property \(\sqrt{ab}=\sqrt{a}\times\sqrt{b}\) (for \(a\geq0,b\geq0\)), we get \(\sqrt{121\times3}=\sqrt{121}\times\sqrt{3}\). Since \(\sqrt{121} = 11\), this becomes \(11\sqrt{3}\).

Step3: Multiply by the coefficient

Now, multiply by the coefficient 10: \(10\times11\sqrt{3}=110\sqrt{3}\).

Answer:

\(110\sqrt{3}\)