\frac{36-\sqrt{36}}{\sqrt{36}}

By evaluating the expression 36 ​ 36 − 36 ​ ​ , we find that it simplifies to 5 after substituting and performing arithmetic operations. The key steps involve calculating the square root of 36, substituting it back into the expression, and simplifying. This exercise is beneficial for building foundational mathematical skills.
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Answered by Anonymous | 2025-07-04

Evaluate the square root: 36 ​ = 6 .
Substitute the value into the expression: 6 36 − 6 ​ .
Simplify the numerator: 36 − 6 = 30 .
Divide to get the final answer: 6 30 ​ = 5 . The final answer is 5 ​ .

Explanation

Understanding the Expression We are asked to evaluate the expression 36 ​ 36 − 36 ​ ​ . This involves finding the square root of 36 and then performing the arithmetic operations.

Evaluating the Square Root First, we need to find the square root of 36. The square root of 36 is 6, since 6 × 6 = 36 . So, 36 ​ = 6 .

Substituting the Value Now, substitute the value of 36 ​ into the expression: 36 ​ 36 − 36 ​ ​ = 6 36 − 6 ​

Simplifying the Numerator Next, we simplify the numerator: 36 − 6 = 30 So the expression becomes: 6 30 ​

Dividing Finally, we divide the numerator by the denominator: 6 30 ​ = 5 Therefore, the value of the expression is 5.

Final Answer The expression 36 ​ 36 − 36 ​ ​ simplifies to 5.


Examples
Imagine you are calculating the efficiency of a simple machine. The expression 36 ​ 36 − 36 ​ ​ could represent a ratio of output to input, where a higher value indicates greater efficiency. In this case, an efficiency of 5 means the machine is quite effective. Understanding how to simplify such expressions helps in analyzing and optimizing real-world systems, from mechanical devices to financial models.

Answered by GinnyAnswer | 2025-07-04