Question

simplify.
$10\sqrt{50}$

Explanation:

Step1: Factor 50 into prime factors

We know that \(50 = 25\times2\), and \(25\) is a perfect square (\(25 = 5^2\)). So we can rewrite \(\sqrt{50}\) as \(\sqrt{25\times2}\).

Step2: Use the property of square roots \(\sqrt{ab}=\sqrt{a}\times\sqrt{b}\) (where \(a\geq0,b\geq0\))

Applying this property, \(\sqrt{25\times2}=\sqrt{25}\times\sqrt{2}\). Since \(\sqrt{25} = 5\), then \(\sqrt{50}=5\sqrt{2}\).

Step3: Multiply by the coefficient 10

Now we have \(10\sqrt{50}=10\times5\sqrt{2}\).

Step4: Calculate \(10\times5\)

\(10\times5 = 50\), so \(10\sqrt{50}=50\sqrt{2}\).

Answer:

\(50\sqrt{2}\)