Evaluate square root of 85

Problem

√(,85)

Solution

1. Identify the number under the radical, which is 85

2. Determine the prime factorization of 85 by checking for small prime factors.

3. Divide by 5 since the number ends in 5 85=5×17

4. Observe that both 5 and 17 are prime numbers.

5. Conclude that since there are no perfect square factors (pairs of prime factors), the radical cannot be simplified further into the form a√(,b)

6. Estimate the decimal value if needed: since 9=81 and 10=100 the value is slightly larger than 9

Final Answer

√(,85)=√(,85)

Want more problems? Check here!