Evaluate square root of 22

Problem

√(,22)

Solution

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

2. Determine if the number is a perfect square. Since 4=16 and 5=25 the value of √(,22) is an irrational number between 4 and 5

3. Factor the radicand to see if it can be simplified. The prime factorization of 22 is 2×11

4. Conclude that since there are no square factors, the expression cannot be simplified further in radical form.

5. Approximate the value using a calculator if a decimal is required. √(,22)≈4.6904157598

Final Answer

√(,22)≈4.6904157598

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