Calculate the square root of 174

Problem

√(,174)

Solution

1. Identify the number under the radical and check for perfect square factors.

2. Find the prime factorization of 174 by dividing by the smallest prime numbers.

174=2×87

174=2×3×29

3. Determine if any factors are repeated. Since 2 3 and 29 are all prime and appear only once, there are no perfect square factors (other than 1 to pull out of the radical.

4. Conclude that the radical expression is already in its simplest radical form.

5. Estimate the decimal value if needed. Since 13=169 and 14=196 the value is slightly larger than 13

√(,174)≈13.1909

Final Answer

√(,174)=√(,174)

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