Calculate the square root of 229

Problem

√(,229)

Solution

1. Identify the number 229 as a prime number. Since 229 is not divisible by any small prime numbers like 2, 3, 5, 7, 11, or 13, it has no perfect square factors other than 1.

2. Estimate the value by finding the nearest perfect squares. Since 15=225 and 16=256 the value of √(,229) must be slightly greater than 15.

3. Calculate the decimal approximation using a calculator or numerical method.

4. State the result in its simplest radical form, which is √(,229) or as a decimal approximation.

Final Answer

√(,229)≈15.13274595

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