Which of the following is irrational?(1 point)
Responses:
3√/4
52.781654292
3.6363636363636363...
−7 8/37
3.6363636363636363...
which of the following correctly defines the term irrational number
Estimate the value of 6×2–√. Which of the following choices is the best estimate?(1 point)
Responses
6.4
6.4
9.8
9.8
8.4
8.4
7.1
Estimate the value of 6×2–√. Which of the following choices is the best estimate?(1 point)
Responses
6.4
6.4
7.1
7.1
8.4
8.4
9.8
Well, let's take a closer look, shall we?
- 3√/4: Well, I hate to break it to you, but there seems to be a bit of a mix-up here. "3√" seems to be incomplete. If you were aiming for the cube root of something, it would be denoted like this: ∛. However, without knowing what exactly is under that root sign, we can't determine if it's rational or not. So, for now, let's set it aside.
- 52.781654292: Ah, a classic decimal number! This one seems to be a precise value, completely expressing all the digits. So, no funny business hiding in there, I'm afraid. It's a rational number.
- 3.6363636363636363...: Ah, the infamous repeating decimal. This little devil suggests that the decimal pattern repeats infinitely, with that "36" sequence going on forever. Tricky, right? But the good news is, repeating decimals can actually be expressed as fractions! So this number is still rational.
- −7 8/37: Well, this looks like a mixed number, with a whole number and a fractional part. But don't let that minus sign fool you, my friend. It just indicates that it's a negative number. As for whether it's rational or not, you betcha! Mixed numbers can always be converted into fractions, so it's still in the rational gang.
So, after carefully analyzing each option, it looks like all of them are rational! They may not be the wildest, most irrational numbers out there, but hey, we can't always have the unexpected.
To determine which of the following numbers is irrational, we need to understand what makes a number irrational. An irrational number is a number that cannot be expressed as a fraction or ratio of two integers.
Let's analyze each option:
1. 3√/4: This is an incomplete expression. It seems to be the cube root (√) of a number divided by 4. Without knowing the specific number under the cube root, we cannot determine if it's rational or irrational.
2. 52.781654292: This is a decimal number, but we don't have enough information to determine if it's rational or irrational.
3. 3.6363636363636363...: This is a repeating decimal where the digits 36 repeat indefinitely. Repeating decimals can always be expressed as a fraction, so it is rational.
4. -7 8/37: This is a mixed number, and we can express it as a fraction. Therefore, it is rational.
Based on the information provided, the number 3.6363636363636363... is rational, but we cannot determine the rationality of the other options without more specific information.
To determine which of the given options is irrational, we need to understand the concept of irrational numbers.
An irrational number is a real number that cannot be expressed as a fraction (ratio) of two integers. These numbers have non-terminating and non-repeating decimal expansions.
Let's examine each option and identify the irrational number:
1) 3√/4: This option is incomplete as it is missing the number under the cube root (√). Without knowing the specific value, we cannot determine if it is irrational or not.
2) 52.781654292: This number is a decimal, but it does not have a pattern of repeating digits. However, it could be rational if it can be expressed as a fraction. To check, we would need to see if it terminates or if the pattern of digits eventually repeats. Without more information, we cannot determine if it is irrational.
3) 3.6363636363636363...: This number has a repeating pattern of decimal digits, specifically the digits 36. Whenever a number has a repeating pattern, it can be expressed as a fraction. Therefore, this option is a rational number and not irrational.
4) -7 8/37: This option represents a mixed fraction, which can be converted into an improper fraction. By doing so, we get -281/37. Again, this is a rational number since it can be expressed as a fraction.
In summary, based on the information provided, we cannot determine which option is irrational as not enough information is given for options 1 and 2. However, options 3 and 4 are known to be rational numbers.