Is the square root of 200 rational
No, the square root of 200 is not rational. It is an irrational number.
Is -33 rational
Yes, -33 is a rational number. A rational number is defined as any number that can be expressed as a fraction where both the numerator and denominator are integers, and the denominator is not zero. Since -33 can be expressed as -33/1, it qualifies as a rational number.
Is -1 / 3 rational
Yes, -1/3 is a rational number. It can be expressed as a fraction where both the numerator (-1) and the denominator (3) are integers. Thus, -1/3 qualifies as a rational number.
No, the square root of 200 is not a rational number. A rational number is a number that can be expressed as the fraction of two integers. However, the square root of 200 is an irrational number because it cannot be expressed as a fraction.
To determine if the square root of 200 is rational, we first need to understand the characteristics of rational and irrational numbers.
A rational number is any number that can be expressed as the quotient or fraction of two integers, where the denominator is not zero. For example, 2/3, 5/2, and -4/7 are all rational numbers.
On the other hand, an irrational number cannot be expressed as a fraction of two integers. Examples of irrational numbers include the square root of 2 (√2), π (pi), and e (Euler's number).
So, the square root of 200 is rational if it can be expressed as a fraction of two integers. To determine this, we can simplify the square root of 200:
√200 = √(2 * 100) = √2 * √100 = 10√2
Now, it is clear that the square root of 200 cannot be written as a fraction of two integers, as it involves the irrational number √2. Therefore, the square root of 200 is irrational, and not rational.