Rewrite as the square of a value: Example: [tex]$0.81 \rightarrow 0.9^2$[/tex]
[tex]$1 \frac{24}{25}$[/tex]
Answer (2)
Convert the mixed number to an improper fraction: 1 25 24 = 25 49 .
Express the numerator and denominator as squares: 25 49 = 5 2 7 2 .
Rewrite the fraction as a square: 5 2 7 2 = ( 5 7 ) 2 .
The number 1 25 24 can be written as the square of 5 7 : 5 7 .
Explanation
Understanding the problem We are given the number 1 25 24 and asked to rewrite it as the square of a value. This means we want to find a number x such that x 2 = 1 25 24 .
Converting to improper fraction First, convert the mixed number to an improper fraction. We have 1 25 24 = 25 1 × 25 + 24 = 25 25 + 24 = 25 49 .
Expressing as a square Now, we want to express 25 49 as the square of a value. We can rewrite the numerator and denominator as squares: 49 = 7 2 and 25 = 5 2 . Thus, we have 25 49 = 5 2 7 2 = ( 5 7 ) 2 .
Final Answer Therefore, 1 25 24 = ( 5 7 ) 2 . We can also write 5 7 as a mixed number: 5 7 = 1 5 2 = 1.4 . So, 1 25 24 = ( 1.4 ) 2 .
Examples
Understanding how to express numbers as squares is fundamental in many areas of mathematics, such as algebra and calculus. For example, when solving quadratic equations, recognizing perfect squares allows us to factor and find solutions easily. In real-world scenarios, this skill is useful in calculating areas and volumes, where dimensions are often squared or cubed. For instance, if you're designing a square garden with an area of 1 25 24 square meters, you'd need to know that each side should be 5 7 meters long.
The mixed number 1 25 24 can be rewritten as the square of the fraction 5 7 , which equals ( 5 7 ) 2 . Additionally, it can also be expressed as ( 1.4 ) 2 . This shows that 1 25 24 is a perfect square of both a fraction and a decimal.
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