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 .
Perform the subtraction: 4 1 .
The simplified expression is 4 1 .
Explanation
Understanding the Problem We are asked to simplify the expression 4 6 − 25 . This involves evaluating the square root, performing subtraction, and then dividing. Let's break it down step by step.
Evaluate the Square Root First, we need to evaluate the square root of 25. The square root of 25 is 5, since 5 × 5 = 25 . So, we have 25 = 5 .
Substitute the Value Now, substitute the value of the square root back into the original expression: 4 6 − 5 .
Perform Subtraction Next, perform the subtraction in the numerator: 6 − 5 = 1 . So the expression becomes 4 1 .
Final Result Finally, we have the simplified expression 4 1 . This is our final answer.
Examples
Understanding how to simplify expressions like this is useful in many areas, such as calculating discounts or figuring out proportions. For example, imagine you have a coupon for a store that gives you $6 off an item, but you have to pay a \sqrt{25} = 5 p rocess in g f ee . I f t h eor i g ina lp r i ce w a s 4 t im es t h e am o u n t yo u p a y a f t er t h e d i sco u n t an df ee , t hi sc a l c u l a t i o n s h o w syo u e n d u pp a y in g \frac{1}{4}$ of the original price after the discount and fee.
