Evaluate square root of 2115

Problem

√(,2115)

Solution

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

2. Factor the number 2115 by checking divisibility. Since the digits sum to $2 + 1 + 1 + 5 = 9,t*h*e*n*u*m*b*e*r*i*s(d(i))*v*i*s(i)*b*l*e*b*y$.

3. Divide 2115 by 9 to find the other factor.

2115=9×235

4. Factor 235 further. Since it ends in 5 it is divisible by 5

235=5×47

5. Rewrite the square root using these factors.

√(,2115)=√(,9×5×47)

6. Simplify the radical by taking the square root of the perfect square 9

√(,9×5×47)=3√(,5×47)

7. Multiply the remaining prime factors inside the radical.

5×47=235

Final Answer

√(,2115)=3√(,235)

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