Evaluate square root of 106

Problem

√(,106)

Solution

1. Identify the number under the radical, which is 106

2. Check for perfect square factors by examining the prime factorization of 106

3. Factor the number into its prime components: 106=2×53

4. Determine if any factors are perfect squares. Since both 2 and 53 are prime numbers and neither is repeated, 106 has no perfect square factors other than 1

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

6. Estimate the decimal value if needed. Since 10=100 and 11=121 the value is between 10 and 11 Using a calculator, √(,106)≈10.2956

Final Answer

√(,106)=√(,106)

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