Square root of 85 simplified
Understand the Problem
The question is asking to simplify the square root of 85, which involves finding any perfect square factors to reduce the expression.
Answer
\( \sqrt{85} \)
Answer for screen readers
The final answer is ( \sqrt{85} )
Steps to Solve
- Identify perfect square factors
85 is not a perfect square itself, so we need to check if it has any perfect square factors. The square factors to consider are: 1, 4, 9, 16, 25, 36, 49, 64, etc.
- Checking the factors of 85
Let's evaluate the divisibility of 85 by perfect squares:
- 85 ÷ 4 = 21.25
- 85 ÷ 9 ≈ 9.44
- 85 ÷ 16 ≈ 5.31
None of these gives a whole number.
- Conclusion: 85 has no perfect square factors
Since 85 has no perfect square factors except 1, the simplest form of the square root of 85 is itself.
Therefore, the square root of 85 simplified is ( \sqrt{85} ).
The final answer is ( \sqrt{85} )
More Information
The square root of 85 is an irrational number and cannot be simplified further.
Tips
A common mistake is to incorrectly identify non-perfect square factors as perfect squares. Always verify the factor by checking if it produces a whole number when the original number is divided by it.
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