Evaluate fifth root of -3125

Problem

√(5,−3125)

Solution

1. Identify the index and the radicand. The index is 5 (an odd number) and the radicand is −3125

2. Determine the sign of the result. Since the index is odd, the fifth root of a negative number is negative.

3. Factor the absolute value of the radicand to find its prime factors.

3125=5×625

3125=5×5×125

3125=5×5×5×25

3125=5×5×5×5×5

4. Rewrite the radicand as a power of 5

3125=5

5. Apply the property of odd roots √(n,−an)=−a

√(5,−3125)=√(5,(−5)5)

6. Simplify the expression.

√(5,(−5)5)=−5

Final Answer

√(5,−3125)=−5

Want more problems? Check here!