The concept of rational numbers is a fundamental idea in mathematics, and it is essential to understand the properties and characteristics of these numbers. A rational number is a number that can be expressed as the ratio of two integers, i.e., a fraction where the numerator and denominator are integers, and the denominator is non-zero. In this article, we will explore whether the square root of 121 is a rational number or not.
To determine if the square root of 121 is rational, we first need to find its value. The square root of 121 is a number that, when multiplied by itself, gives 121. This number is 11, as 11 × 11 = 121. Now, we need to check if 11 can be expressed as a ratio of two integers.
Definition and Properties of Rational Numbers
A rational number is a number that can be written in the form $\frac{a}{b}$, where $a$ and $b$ are integers, and $b$ is non-zero. Rational numbers can be expressed as terminating or recurring decimals. For example, $\frac{1}{2}$ = 0.5, $\frac{1}{3}$ = 0.333..., and $\frac{22}{7}$ = 3.142857....
Some essential properties of rational numbers include:
- Rational numbers can be added, subtracted, multiplied, and divided.
- The result of these operations is always a rational number.
- Rational numbers can be expressed in their simplest form.
Is the Square Root of 121 Rational?
As we have already determined, the square root of 121 is 11. Now, we need to check if 11 is a rational number. Since 11 can be expressed as $\frac{11}{1}$, where 11 and 1 are integers, and 1 is non-zero, 11 is indeed a rational number.
This conclusion is based on the definition of rational numbers. As 11 satisfies this definition, we can confidently say that the square root of 121 is a rational number.
Evidence and Examples
| Number | Square Root | Rational or Irrational |
|---|---|---|
| 121 | 11 | Rational |
| 16 | 4 | Rational |
| 2 | $\sqrt{2}$ | Irrational |
The table above provides some examples of numbers, their square roots, and whether they are rational or irrational. As shown, the square root of 121 is 11, which is rational, while the square root of 2 is irrational.
Key Points
- The square root of 121 is 11.
- 11 can be expressed as a ratio of two integers, $\frac{11}{1}$.
- The square root of 121 is a rational number.
- Rational numbers can be expressed as terminating or recurring decimals.
- The properties of rational numbers include addition, subtraction, multiplication, and division.
Conclusion
In conclusion, the square root of 121 is indeed a rational number. This is because 11, the square root of 121, can be expressed as a ratio of two integers, satisfying the definition of a rational number. Understanding the properties and characteristics of rational numbers is crucial in mathematics, and this knowledge can be applied to various mathematical operations and theories.
FAQs
What is a rational number?
+A rational number is a number that can be expressed as the ratio of two integers, i.e., a fraction where the numerator and denominator are integers, and the denominator is non-zero.
Is the square root of 121 an integer?
+Yes, the square root of 121 is 11, which is an integer.
Can all square roots be expressed as rational numbers?
+No, not all square roots can be expressed as rational numbers. For example, the square root of 2 is an irrational number.