Question

Simplify the radical expression. $$ \sqrt{60} $$

Short answer

\(\sqrt{60}\) simplifies to \(2\sqrt{15}\).

Step-by-step solution

Find Prime Factors

Start by finding the prime factors of 60. It can be broken down into two factors as follows \[60 = 6 * 10\]. Both these can be further broken down: \[6 = 2 * 3\] and \[10 = 2 * 5\]. Thus, the prime factorization of 60 is \(2 * 2 * 3 * 5\). Both of the 2's are a pair, which makes them a perfect square.

Take out the Perfect Square

Take this perfect square (i.e., \(2*2\)), square root it and take it out from under the square root symbol. This leaves the other factors (i.e., 3 and 5) which multiply to 15, under the square root. The square root of \(2*2\) is 2. So now, the expression can be written as \[2\sqrt{15}\]. This cannot be simplified further as 15 does not have any perfect square factors.

Write Final Answer

So \(\sqrt{60}\) simplifies to \[2\sqrt{15}\]. This is the final simplified form of the radical expression.