Is the square root of 121 rational or irrational?
Understand the Problem
The question is asking whether the square root of 121 is a rational or irrational number. To solve this, we recall that a rational number can be expressed as the quotient of two integers, while an irrational number cannot. The square root of 121 is a whole number, which is rational.
Answer
The square root of 121 is a rational number.
Answer for screen readers
The square root of 121 is a rational number.
Steps to Solve
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Identify the Square Root First, we need to calculate the square root of 121. The square root is denoted by the symbol $\sqrt{}$.
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Calculate the Square Root Now, let's find the square root: $$ \sqrt{121} = 11 $$
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Determine Rationality Next, we need to determine if 11 is a rational or irrational number. Since a rational number can be expressed as a fraction of two integers (for example, $\frac{11}{1}$), we conclude that 11 is a rational number.
The square root of 121 is a rational number.
More Information
The square root of 121 is 11, which is a whole number and can be expressed as a fraction. This means it is classified as rational. Fun fact: The square root of any perfect square (like 121) is always a whole number and hence rational!
Tips
- A common mistake is to assume that all square roots are irrational. In fact, only the square roots of non-perfect squares (like 2 or 3) are irrational.
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