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 number or an irrational number. To solve this, we need to determine the value of the square root and check if it can be expressed as a fraction of two integers.
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
- Calculate the square root of 121
We need to find the value of $\sqrt{121}$. The square root of a number is a value that, when multiplied by itself, gives that number.
- Determine the value obtained
Calculating the square root, we find: $$ \sqrt{121} = 11 $$
- Check if the result is a rational number
A rational number is defined as a number that can be expressed as a fraction of two integers. Since 11 can be expressed as $\frac{11}{1}$, it is considered a rational number.
The square root of 121 is a rational number.
More Information
The square root of a perfect square like 121 always yields a rational number. In this case, since 121 is $11^2$, the square root is simply 11.
Tips
- Mistaking the square root of a non-perfect square for a rational number (e.g., $\sqrt{2}$ is irrational). Always verify if the number is a perfect square first.
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