Evaluate square root of 117

Problem

√(,117)

Solution

1. Identify the number under the radical and check for perfect square factors.

2. Find the prime factorization of 117 by checking divisibility. Since the sum of the digits 1 + 1 + 7 = 9i*s(d(i))*v*i*s(i)*b*l*e*b*y,t*h*e*n*u*m*b*e*r17i*s(d(i))*v*i*s(i)*b*l*e*b*y$.

3. Factor the expression into a product of a perfect square and another integer.

117=9×13

4. Apply the product property of radicals, which states √(,a×b)=√(,a)×√(,b)

√(,117)=√(,9×13)

√(,117)=√(,9)×√(,13)

5. Simplify the square root of the perfect square 9

√(,9)=3

Final Answer

√(,117)=3√(,13)

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