Question

simplify.
$9\sqrt{50}$

Explanation:

Step1: Factor 50 into perfect square and other

We know that \(50 = 25\times2\), and \(25\) is a perfect square (\(25 = 5^{2}\)). So we can rewrite \(\sqrt{50}\) as \(\sqrt{25\times2}\).
Using the property of square roots \(\sqrt{ab}=\sqrt{a}\times\sqrt{b}\) (where \(a = 25\), \(b = 2\) and \(a\geq0,b\geq0\)), we get \(\sqrt{25\times2}=\sqrt{25}\times\sqrt{2}\).
Since \(\sqrt{25} = 5\), then \(\sqrt{50}=5\sqrt{2}\).

Step2: Multiply with the coefficient 9

Now we have \(9\sqrt{50}\), substitute \(\sqrt{50}=5\sqrt{2}\) into it, we get \(9\times5\sqrt{2}\).
Calculate \(9\times5 = 45\), so \(9\sqrt{50}=45\sqrt{2}\).

Answer:

\(45\sqrt{2}\)