Question

simplify.
\sqrt{242}

Explanation:

Step1: Factor 242

Factor 242 into prime factors: \(242 = 2\times121 = 2\times11^2\)

Step2: Simplify the square root

Using the property \(\sqrt{ab}=\sqrt{a}\cdot\sqrt{b}\) (for \(a\geq0,b\geq0\)):
\(\sqrt{242}=\sqrt{2\times11^2}=\sqrt{11^2}\cdot\sqrt{2}=11\sqrt{2}\)

Answer:

\(11\sqrt{2}\)