Problem

Simplify. Remove all perfect squares from inside the square root. \[ \sqrt{108}= \]

Solution

Step 1 :First, find the prime factors of 108. They are 2, 2, 3, 3, 3.

Step 2 :Next, pair the prime factors into groups of two. We have two pairs: (2, 2) and (3, 3), leaving one 3 unpaired.

Step 3 :The product of the pairs, which represent the perfect squares, is 6. The product of the unpaired factors is 3.

Step 4 :Therefore, the simplified form of the square root of 108 is 6 times the square root of 3.

Step 5 :Final Answer: \(\boxed{6\sqrt{3}}\)

From Solvely APP
Source: https://solvelyapp.com/problems/42838/

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