$\sqrt{\frac{13}{100}}$
Answer (1)
Rewrite the expression as a fraction of square roots: 100 13 = 100 13 .
Simplify the denominator: 100 = 10 .
The simplified expression is 10 13 .
The final answer is 10 13 .
Explanation
Understanding the Problem We are given the expression 100 13 . Our goal is to simplify this expression.
Rewriting the Expression We can rewrite the expression as a fraction of square roots: 100 13 = 100 13
Simplifying the Denominator Now, we simplify the denominator. We know that 100 = 10 , so we have: 100 13 = 10 13
Final Answer The simplified expression is 10 13 . Since 13 is a prime number, 13 cannot be simplified further. Therefore, our final answer is 10 13 .
Examples
Square roots appear in various real-world scenarios, such as calculating distances using the Pythagorean theorem. For example, if you have a square garden with an area of 100 13 square meters, finding the side length involves taking the square root of the area. In this case, the side length would be 100 13 = 10 13 meters. This concept is also crucial in physics, engineering, and computer graphics for calculating magnitudes and distances.
