Simplify square root of 313

Problem

√(,313)

Solution

1. Check for divisibility by small prime numbers. Since 313 is odd, it is not divisible by 2 The sum of the digits is 3 + 1 + 3 = 7,w*h*i*c*h*i*s(n)*o*t*d(i)*v*i*s(i)*b*l*e*b*y,s(o)13i*s(n)*o*t*d(i)*v*i*s(i)*b*l*e*b*y.I*t*d(o)*e*s(n)*o*t*e*n*d(i)*no*r,s(o)*i*t*i*s(n)*o*t*d(i)*v*i*s(i)*b*l*e*b*y$.

2. Test larger primes up to the square root of the number. Since √(,313)≈17.69 we test primes up to 17

3. Divide by 7 313÷7=44.71... (No).

4. Divide by 11 313÷11=28.45... (No).

5. Divide by 13 313÷13=24.07... (No).

6. Divide by 17 313÷17=18.41... (No).

7. Conclude that since 313 has no prime factors less than or equal to its square root, 313 is a prime number.

8. Determine that because 313 is prime, it has no perfect square factors other than 1 Therefore, the radical cannot be simplified further.

Final Answer

√(,313)=√(,313)

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