Which of the following is a rational number? square root of 15, square root of 16, square root of 17, square root of 18
The correct answer and explanation is:
The correct answer is the square root of 16.
A rational number is any number that can be expressed as a fraction, where both the numerator and denominator are integers. Rational numbers include whole numbers, fractions, and decimals that either terminate or repeat.
Now, let’s examine each option:
- Square root of 15: The square root of 15 is an irrational number because 15 is not a perfect square. The square root of a non-perfect square cannot be expressed as a simple fraction or a terminating or repeating decimal. The square root of 15 is approximately 3.872, which continues without any repeating pattern. Therefore, it is an irrational number.
- Square root of 16: The square root of 16 is 4, which is a whole number. Whole numbers are a subset of rational numbers because they can be expressed as fractions (e.g., 4/1). Since 4 is an integer, the square root of 16 is a rational number.
- Square root of 17: Similar to the square root of 15, the square root of 17 is also irrational because 17 is not a perfect square. The square root of 17 is approximately 4.123, and it continues without repeating or terminating, making it an irrational number.
- Square root of 18: The square root of 18 is an irrational number as well. While it can be simplified as 3√2, this expression still represents an irrational number because the square root of 2 is irrational. Therefore, the square root of 18 is not rational.
In conclusion, the square root of 16 is the only rational number among the choices because its square root results in a whole number.