Simplify: $(\sqrt{25}-4)^3 \cdot 5$
Answer (1)
Evaluate the square root: 25 = 5 .
Substitute the value into the expression: ( 5 − 4 ) 3 ⋅ 5 .
Simplify the parenthesis: ( 1 ) 3 ⋅ 5 .
Evaluate the power and multiply: 1 ⋅ 5 = 5 . The simplified expression is 5 .
Explanation
Evaluate the square root We are asked to simplify the expression ( 25 − 4 ) 3 ⋅ 5 . Let's break this down step by step. First, we need to evaluate the square root.
Substitute the value The square root of 25 is 5, so we have 25 = 5 . Now, substitute this value back into the original expression: ( 5 − 4 ) 3 ⋅ 5 .
Simplify the parenthesis Next, we simplify the expression inside the parenthesis: 5 − 4 = 1 . So the expression becomes ( 1 ) 3 ⋅ 5 .
Evaluate the power Now, we evaluate the power: 1 3 = 1 ⋅ 1 ⋅ 1 = 1 . The expression is now 1 ⋅ 5 .
Multiply by 5 Finally, we multiply the result by 5: 1 ⋅ 5 = 5 . Therefore, the simplified expression is 5.
Examples
Understanding how to simplify expressions like this is useful in many areas, such as calculating the volume of a cube or determining the final amount in a savings account with simple interest. For instance, if you were calculating the volume of a cube with sides defined by a similar expression, simplifying would be a necessary step. Also, in financial calculations, simplifying expressions helps in quickly determining outcomes without complex computations. This skill is fundamental in both mathematical and real-world problem-solving.
