Question

question
express in simplest radical form.
\sqrt{160}

Explanation:

Step1: Factor the radicand

We factor 160 into a product of a perfect square and another number. We know that \(160 = 16\times10\), where 16 is a perfect square. So, \(\sqrt{160}=\sqrt{16\times10}\).

Step2: Use the property of square roots

Using the property \(\sqrt{ab}=\sqrt{a}\times\sqrt{b}\) (where \(a\geq0\) and \(b\geq0\)), we can rewrite \(\sqrt{16\times10}\) as \(\sqrt{16}\times\sqrt{10}\).

Step3: Simplify the perfect square root

Since \(\sqrt{16} = 4\), we substitute that in. So, \(\sqrt{16}\times\sqrt{10}=4\sqrt{10}\).

Answer:

\(4\sqrt{10}\)