square root of 82 simplified
Understand the Problem
The question is asking to simplify the square root of 82, which involves finding any perfect square factors of 82 to simplify the expression.
Answer
The simplified form of the square root of 82 is \( \sqrt{82} \) and its approximate value is \( 9.055 \).
Answer for screen readers
The simplified form of the square root of 82 is ( \sqrt{82} ) and its approximate value is ( 9.055 ).
Steps to Solve
- Identify Factors of 82
First, let's find the factors of 82. The prime factorization of 82 is:
$$ 82 = 2 \times 41 $$
- Look for Perfect Squares
Next, we check if any of the factors are perfect squares. A perfect square is a number that can be expressed as the square of an integer. The only perfect square factors of 82 are 1 and 4, but none of these contribute to simplification as 2 and 41 are not perfect squares.
- Simplifying the Square Root
Since there are no perfect square factors of 82 other than 1, we cannot simplify the square root further. Therefore, the square root of 82 remains as:
$$ \sqrt{82} $$
- Expressing the Answer
Finally, we can write the square root of 82 in terms of a decimal if needed, which will be approximately:
$$ \sqrt{82} \approx 9.055 $$
The simplified form of the square root of 82 is ( \sqrt{82} ) and its approximate value is ( 9.055 ).
More Information
The number 82 is itself not a perfect square, and it is the product of the prime numbers 2 and 41. Since there are no perfect square factors to simplify the square root, it remains ( \sqrt{82} ).
Tips
- Assuming that since 82 is close to 81 (which is a perfect square), it can be simplified. Remember, you can only simplify square roots by finding the product of perfect square factors.