9. Name all of the following numbers that are irrational.
2/3,√8,√144,5.2,0.(87) ̅,π
I think it's just pi.
Is that correct?
Thank You
√8 is also irrational
2^2 = 4, 3^2=9, but there's no rational number x such that x^2 = 8
The square root of 8 is also irrational.
Thank you...I should have figured that out...
Yes, you are correct. π (pi) is the only number among the given options that is irrational.
To understand why π is irrational, we need to know that a number is considered irrational if it cannot be expressed as a fraction of two integers (i.e., it cannot be written as a ratio). π is an irrational number because it is a non-repeating and non-terminating decimal.
Now let's look at the other numbers you mentioned:
2/3: This number is a rational number because it can be expressed as the fraction 2/3.
√8: The square root of 8 is approximately 2.8284. However, this number can be expressed as a simplified fraction (√8 = 2√2) and is, therefore, a rational number.
√144: The square root of 144 is exactly 12, which can be expressed as the fraction 12/1. Thus, √144 is a rational number.
5.2: This is also a rational number because it can be expressed as the fraction 52/10 or simplified as 26/5.
0.(87) ̅: This number is a repeating decimal, as indicated by the bar over the 87. However, it can still be expressed as a fraction: 0.(87) ̅ = 87/99. Therefore, it is a rational number.
So, out of all the numbers you mentioned, only π is irrational.