Question

simplify:
\sqrt{250}
\text{ a) } 2\sqrt{5}
\text{ b) } 5\sqrt{2}
\text{ c) } 5\sqrt{10}
\text{ d) } 10\sqrt{5}

Explanation:

Step1: Factor 250

Factor 250 into a perfect square and another number: \(250 = 25\times10\)

Step2: Apply square root property

Use \(\sqrt{ab}=\sqrt{a}\times\sqrt{b}\) (\(a\geq0,b\geq0\)): \(\sqrt{250}=\sqrt{25\times10}=\sqrt{25}\times\sqrt{10}\)

Step3: Simplify \(\sqrt{25}\)

\(\sqrt{25} = 5\), so \(\sqrt{25}\times\sqrt{10}=5\sqrt{10}\)

Answer:

c. \(5\sqrt{10}\)