Evaluate square root of 105
Problem
Solution
Identify the number under the radical, which is
105 Determine the prime factorization of
105 to see if there are any perfect square factors.Divide by the smallest prime factor,
3 105=3×35 Divide
35 by its smallest prime factor,5 35=5×7 Observe that the prime factorization is
3×5×7 Since there are no repeating prime factors, there are no perfect square factors other than1 Conclude that the radical cannot be simplified further into a simpler radical form.
Approximate the value using a calculator if a decimal is required:
√(,100)=10 and√(,121)=11 so the value is between10 and11
Final Answer
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