Simplify square root of 195

Problem

√(,195)

Solution

1. Identify the number under the radical, which is 195

2. Find the prime factorization of 195 by checking for small prime factors.

3. Divide by 3 because the sum of the digits (1+9+5=15 is divisible by 3

195=3×65

4. Divide 65 by 5 because it ends in 5

65=5×13

5. List the prime factors of 195

195=3×5×13

6. Determine if there are any perfect square factors. Since all prime factors (3, 5, 13)a*r*e*u*n*i*q*u*e*a*n*d(h)*a*v*e*a*n*e*x*p*o*n*e*n*t*o*ƒ,t*h*e*r*e*a*r*e*n*o*p*e*r*ƒ*e*c*t*s(q)*u*a*r*e*ƒ*a*c*t*o*r*s(o)*t*h*e*r*t*h*a*n$.

7. Conclude that the radical cannot be simplified further into the form a√(,b)

Final Answer

√(,195)=√(,195)

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