QQuestionMathematics
QuestionMathematics
Is the square root of 6.25 a rational or irrational number? Explain your reasoning.
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Answer
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Step 1:I'll solve this step by step with precise mathematical reasoning:
Step 2:: Understand the definition of rational and irrational numbers
- A rational number is a number that can be expressed as a fraction $$\frac{p}{q}$$, where $$p$$ and $$q$$ are integers and $$q \neq 0
- An irrational number cannot be expressed as a simple fraction of integers
Step 3:: Simplify the square root
\sqrt{6.25} = \sqrt{\frac{625}{100}} = \frac{\sqrt{625}}{\sqrt{100}} = \frac{25}{10} = 2.5
Step 4:: Analyze the result
- $$2.5$$ can be written as the fraction $$\frac{5}{2}
- Since 2.5 can be expressed as a ratio of two integers, \sqrt{6.25} is a rational number
Step 5:: Verify the rationality
- $$\sqrt{6.25} = 2.5
- 2.5 = \frac{5}{2}, which is a rational number
Final Answer
\sqrt{6.25} is a rational number because it can be expressed as the fraction \frac{5}{2}.
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