Simplify square root of 22

Problem

√(,22)

Solution

1. Identify the number under the radical, which is 22

2. Find the prime factorization of 22 by dividing by the smallest prime numbers.

3. Determine that 22=2×11

4. Check for perfect square factors within the prime factorization. Since both 2 and 11 are prime and appear only once, there are no perfect square factors other than 1

5. Conclude that the radical cannot be simplified further into a form a√(,b) where b is a smaller integer.

Final Answer

√(,22)=√(,22)

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