Evaluate square root of 130

Problem

√(,130)

Solution

1. Identify the number under the radical, which is 130

2. Check for perfect square factors by looking at the prime factorization of 130

3. Factor the number into its prime components: 130=2×5×13

4. Determine if any factors are repeated. Since all prime factors are unique, there are no perfect square factors other than 1

5. Conclude that the radical cannot be simplified further into a simpler radical form.

6. Approximate the value if a decimal is required. Since 11=121 and 12=144 the value is between 11 and 12

Final Answer

√(,130)≈11.40175

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