Question

question
express in simplest radical form.
\\(\sqrt{200}\\)
answer attempt 1 out of 2

Explanation:

Step1: Factor 200

We know that \(200 = 100\times2\), and \(100\) is a perfect square. So we can rewrite \(\sqrt{200}\) as \(\sqrt{100\times2}\).

Step2: Use the property of square roots

Using the property \(\sqrt{ab}=\sqrt{a}\times\sqrt{b}\) (where \(a = 100\) and \(b = 2\) and \(a\geq0,b\geq0\)), we get \(\sqrt{100\times2}=\sqrt{100}\times\sqrt{2}\).
Since \(\sqrt{100} = 10\), then \(\sqrt{100}\times\sqrt{2}=10\sqrt{2}\).

Answer:

\(10\sqrt{2}\)