Question

question express in simplest radical form. \\(sqrt{180}\\) answer attempt 1 out of 2 submit answer

Explanation:

Step1: Factor 180 into prime factors

We need to express 180 as a product of prime factors. We know that \(180 = 2\times90=2\times2\times45 = 2\times2\times3\times15=2\times2\times3\times3\times5\). So, \(180 = 2^{2}\times3^{2}\times5\).

Step2: Apply the square - root property

The square - root property states that \(\sqrt{ab}=\sqrt{a}\times\sqrt{b}\) for \(a\geq0\) and \(b\geq0\), and \(\sqrt{a^{2}} = a\) for \(a\geq0\).
We have \(\sqrt{180}=\sqrt{2^{2}\times3^{2}\times5}\).
Using the property \(\sqrt{ab}=\sqrt{a}\times\sqrt{b}\), we can rewrite it as \(\sqrt{2^{2}}\times\sqrt{3^{2}}\times\sqrt{5}\).
Since \(\sqrt{2^{2}} = 2\) and \(\sqrt{3^{2}}=3\), we get \(2\times3\times\sqrt{5}\).

Step3: Simplify the product

Calculate \(2\times3 = 6\). So, \(\sqrt{180}=6\sqrt{5}\).

Answer:

\(6\sqrt{5}\)