Calculate the square root of 145
Problem
Solution
Identify the number under the radical, which is
145 Check for perfect square factors by finding the prime factorization of
145 Divide by the smallest prime numbers:
145 is not divisible by2 or3 Divide by
5 145=5×29 Observe that both
5 and29 are prime numbers and neither is a perfect square.Conclude that the square root cannot be simplified into a simpler radical form.
Estimate the value: since
12=144 and13=169 the value is slightly larger than12 Calculate the decimal approximation:
√(,145)≈12.04159
Final Answer
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