Evaluate 8 square root of 591

Problem

8√(,591)

Solution

1. Identify the number under the radical, which is 591

2. Check for prime factors to see if the square root can be simplified. We test small prime numbers: 591 is not divisible by 2 (it is odd). The sum of the digits is 5 + 9 + 1 = 15,w*h*i*c*h*i*s(d(i))*v*i*s(i)*b*l*e*b*y,s(o)91i*s(d(i))*v*i*s(i)*b*l*e*b*y$.

3. Divide 591 by 3

591÷3=197

4. Check if 197 is prime or has square factors. Testing primes up to √(,197)≈14 197 is not divisible by 2,3,5,7,11, or *13 Therefore, 197 is prime.

5. Conclude that since 591=3×197 and neither factor is a perfect square nor contains a perfect square factor, the radical √(,591) cannot be simplified further into integer components.

6. Determine the decimal approximation if required. Since √(,576)=24 and √(,625)=25 √(,591) is approximately 24.31

7. Multiply the approximation by 8

8×24.31049...≈194.4839

Final Answer

8√(,591)=8√(,591)

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