Which of these is an irrational number.
A. √150
B. √441
C. √200
D. √250
Ok I worked it out like this
√150= 12.24 (12)
√441= 21.07 (21)
√200= 14.14 (14)
√250= 15.81 (16)
Ok I can't figure this out. What exactly does rational and irrational mean I'm getting so confused right now. Could someone help me understand? I have two others that I needed help with but I want to understand this one first. Please help me to understand. I would appreciate it very very much. I feel so lost right now....
the actual question is which one is a rational number, so, thank you bosnian.
An irrational number is a real number that cannot be written as a simple fraction.
√150 = √ ( 25 * 6 ) = √25 * √6 = 5 √6
√6 cannot be written as a simple fraction so √150 = 5 √6 is an irrational number
√441 = √ (21^2 ) = 21
√200 = √ (100 * 2 ) = √100 √2 = 10 √2
√2 cannot be written as a simple fraction so √200 = 10 √2 is an irrational number
√250 = √ ( 25 * 10 ) = √25 √10 = 5 √10
√10 cannot be written as a simple fraction so √250 = 5 √10 is an irrational number
√150 , √200 and √250 are an irrational numbers.
Are yall really asking which is a Rational number? there's four numbers
A) 150
B) 441
C) 200
D) 250
And he said 150 200 and 250 are irrational, so CLEARLY 441 is a rational number, how dumb
Ok I'm still lost I only can choose one answer. I'm so confused
Hey there! Don't worry, I'm here to help you out and hopefully make you smile along the way!
Rational and irrational numbers can be a bit tricky, but I promise it's not as scary as it seems. Let's break it down:
A rational number is any number that can be expressed as a fraction or a ratio of two integers. For example, 1.5 can be written as 3/2, so it's a rational number.
An irrational number, on the other hand, is a number that cannot be expressed as a fraction or a ratio of two integers. They go on and on forever without repeating. The most well-known example is probably π (pi). It goes on and on, never settling into a repeating pattern.
So, in this case, we're looking for the irrational number among the options. To determine that, all we need to do is see if we can simplify the square roots:
A. √150 ≈ 12.247. Since this doesn't simplify to a whole number or a fraction, it is an irrational number.
B. √441 ≈ 21. This simplifies to a whole number, so it is a rational number.
C. √200 ≈ 14.142. This doesn't simplify to a whole number or a fraction, so it is an irrational number.
D. √250 ≈ 15.811. Similarly, this doesn't simplify to a whole number or a fraction, so it is an irrational number.
So, the answer is A. √150 is an irrational number. Keep up the good work, and if you have any more questions, feel free to ask!
I can definitely help you understand the concepts of rational and irrational numbers.
In mathematics, a rational number is any number that can be expressed as a fraction (the ratio of two integers). Rational numbers can be written as terminating decimals (where the digits stop after a certain point) or repeating decimals (where a pattern of digits repeats infinitely). Examples of rational numbers include 1/2, 3/4, 0.25, and -2/3.
On the other hand, an irrational number is a number that cannot be expressed as a fraction. Irrational numbers have non-terminating and non-repeating decimal representations. The square root of a non-perfect square is an example of an irrational number. These numbers go on forever without repeating any pattern. Pi (π) and the square root of 2 (√2) are examples of irrational numbers.
Now, let's apply this knowledge to identify which of the given options is an irrational number.
Option A: √150
To simplify √150, we can factorize 150 into its prime factorization: 150 = 2 * 3^1 * 5^2.
Therefore, √150 = √(2 * 3^1 * 5^2) = 5√6.
Since this is not a perfect square (the square root of 6 is not an integer), it is an irrational number.
Option B: √441
Since 441 is a perfect square (21 * 21), √441 is a rational number. It equals exactly 21.
Option C: √200
To simplify √200, we can factorize 200 into its prime factorization: 200 = 2^3 * 5^2.
Therefore, √200 = √(2^3 * 5^2) = 10√2.
Like option A, this is not a perfect square, so it is an irrational number.
Option D: √250
To simplify √250, we can factorize 250 into its prime factorization: 250 = 2 * 5^3.
Therefore, √250 = √(2 * 5^3) = 5√10.
Again, this is not a perfect square, so it is an irrational number.
So, the answer to your question is that options A, C, and D (√150, √200, and √250) are all irrational numbers. Option B (√441) is a rational number.