Simplify [tex]$\frac{6-\sqrt{25}}{4}=$\square[/tex]
Answer (1)
Evaluate the square root: 25 = 5 .
Substitute the value into the expression: 4 6 − 5 .
Simplify the numerator: 6 − 5 = 1 .
Divide to get the final result: 4 1 .
Explanation
Understanding the Problem We are asked to simplify the expression 4 6 − 25 . This involves evaluating the square root and then performing the arithmetic operations.
Evaluating the Square Root First, we need to evaluate the square root of 25. Since 5 × 5 = 25 , we have 25 = 5 .
Substituting the Value Now we substitute this value back into the original expression: 4 6 − 25 = 4 6 − 5
Simplifying the Numerator Next, we simplify the numerator: 6 − 5 = 1 So the expression becomes: 4 1
Final Result Therefore, the simplified expression is 4 1 .
Examples
Understanding how to simplify radical expressions is a fundamental skill in algebra. For example, if you are calculating the area of a square with side length 6 − 25 , you would need to simplify this expression first to find the actual side length, which is 1. Then, the area would be 1 2 = 1 . This type of simplification is also useful in physics when dealing with distances or forces that involve square roots.
