Evaluate square root of 185

Problem

√(,185)

Solution

1. Identify the number under the radical, which is 185

2. Check for perfect square factors by finding the prime factorization of 185

3. Divide by the smallest prime factor, 5 which gives 185=5×37

4. Observe that both 5 and 37 are prime numbers and neither is a perfect square.

5. Conclude that since there are no repeated prime factors, the square root cannot be simplified into a simpler radical form.

6. Approximate the value if a decimal is required. Since 13=169 and 14=196 the value is between 13 and 14 Using a calculator, √(,185)≈13.60147

Final Answer

√(,185)=√(,185)

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