Determine if √16 is rational or irrational and give a reason for your answer.
√16 is rational.
A rational number is defined as any number that can be expressed as the quotient or fraction p/q of two integers, where q is not equal to 0.
In this case, √16 can be simplified as √(4*4), which is equal to 4. 4 can be expressed as the quotient of two integers, 4/1. Therefore, √16 can be expressed as a fraction of two integers and is therefore rational.
To determine if √16 is rational or irrational, we need to analyze if it can be expressed as a ratio of two integers, which is a characteristic of rational numbers, or if it cannot be expressed as a ratio of two integers, which characterizes irrational numbers.
First, calculate the square root of 16: √16 = 4.
Since 4 can be expressed as 4/1, which is a ratio of two integers, it is considered a rational number.
Therefore, √16 is rational.
To determine if √16 is rational or irrational, we need to understand the terms rational and irrational numbers.
A rational number is any number that can be expressed as a fraction, where both the numerator and the denominator are integers. In other words, it can be written as a ratio of two integers.
An irrational number is a number that cannot be expressed as a fraction, that is, it cannot be written as a ratio of two integers. Irrational numbers are non-repeating and non-terminating decimal numbers.
Now, let's find out if √16 is rational or irrational.
To √16, we need to find the square root of 16. The square root of a number is a value that, when multiplied by itself, gives the original number.
√16 = √(4 * 4) = 4
Since 4 is an integer, √16 can be written as the ratio of two integers. Therefore, √16 is a rational number.
In summary, √16 is rational because it can be expressed as a fraction or ratio of two integers (4/1).