Simplify square root of 527

Problem

√(,527)

Solution

1. Check for divisibility by small prime numbers to find factors. Since 527 is odd, it is not divisible by 2 The sum of the digits is 5 + 2 + 7 = 14,w*h*i*c*h*i*s(n)*o*t*d(i)*v*i*s(i)*b*l*e*b*y,s(o)27i*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 √(,527)≈22.95 we test primes up to 19

3. Divide 527 by 7 527÷7≈75.28

4. Divide 527 by 11 527÷11≈47.9

5. Divide 527 by 13 527÷13≈40.53

6. Divide 527 by 17 527÷17=31

7. Identify the factors of the radicand. We found that 527=17×31

8. Determine if simplification is possible. Since both 17 and 31 are prime numbers and neither is a perfect square, there are no square factors to pull out of the radical.

Final Answer

√(,527)=√(,527)

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