Calculate the square root of 154

Problem

√(,154)

Solution

1. Identify the number under the radical, which is 154

2. Find the prime factorization of 154 to see if there are any perfect square factors.

3. Divide by the smallest prime number, 2

154=2×77

4. Divide 77 by its smallest prime factor, 7

77=7×11

5. Analyze the prime factors:

154=2×7×11

6. Conclude that since there are no repeating prime factors, 154 has no perfect square factors other than 1

7. Determine that the square root cannot be simplified further in radical form.

8. Approximate the value using a calculator if a decimal is required:

√(,154)≈12.40967

Final Answer

√(,154)=√(,154)

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