Express in simplest radical form.start fraction, square root of, 180, end square root, divided by, 6, end fraction6180

Question

Express in simplest radical form:

$\frac{\sqrt{180}}{6}$

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Solution

First, let's simplify the square root of 180. The prime factorization of 180 is 22335. Group them into pairs: (22) and (33). The square root of each pair is 2 and 3 respectively. So, the square root of 180 simplifies to 23sqrt(5) = 6sqrt(5).

Now, let's divide this by 6: 6sqrt(5) / 6 = sqrt(5).

So, the simplest radical form of the given expression is sqrt(5).

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Express in simplest radical form.start fraction, square root of, 180, end square root, divided by, 6, end fraction6180​ ​

Question