The irrational numbers are numbers that cannot be expressed as a fraction or a ratio of two integers.
Out of the given options, the number 3.6363636363636363... is irrational.
To explain why, we can understand that this decimal representation continues indefinitely with the pattern of repeating decimal digits. Any repeating decimal can be converted into a fraction, so if 3.6363636363636363... were rational, we could express it as a fraction. However, since the decimal continues indefinitely with the repeating pattern, there is no finite fraction that represents this number. Thus, 3.6363636363636363... is irrational.
Which of the following is irrational?
V3/4
53.781654292
3.6363636363636363…
-7 8/4
Explain why.
5 answers
Wrong.
Apologies for the incorrect response.
The correct answer is:
Out of the given options, the number 3.6363636363636363... is irrational.
To explain why, we can understand that this decimal representation continues indefinitely with the pattern of repeating decimal digits. Any repeating decimal can be converted into a fraction, so if 3.6363636363636363... were rational, we could express it as a fraction. However, we can simplify the repeating decimal as follows:
Let x = 3.636363...
Then 100x = 363.636363...
By subtracting the equation "100x = 363.636363..." from "x = 3.636363...", we get:
99x = 360
x = 360/99
Since 360 and 99 share no common factors other than 1, the fraction 360/99 is in its simplest form and cannot be further reduced. Therefore, 3.636363... is a repeating decimal that cannot be expressed as a fraction of two integers, making it irrational.
The correct answer is:
Out of the given options, the number 3.6363636363636363... is irrational.
To explain why, we can understand that this decimal representation continues indefinitely with the pattern of repeating decimal digits. Any repeating decimal can be converted into a fraction, so if 3.6363636363636363... were rational, we could express it as a fraction. However, we can simplify the repeating decimal as follows:
Let x = 3.636363...
Then 100x = 363.636363...
By subtracting the equation "100x = 363.636363..." from "x = 3.636363...", we get:
99x = 360
x = 360/99
Since 360 and 99 share no common factors other than 1, the fraction 360/99 is in its simplest form and cannot be further reduced. Therefore, 3.636363... is a repeating decimal that cannot be expressed as a fraction of two integers, making it irrational.
The answer is v3/4 explain why
Apologies for the confusion. Let's discuss why V3/4 is irrational.
To determine if V3/4 is rational or irrational, we need to check if we can simplify it into a fraction of two integers.
To simplify V3/4, we need to find a fraction where the numerator and denominator have no common factors other than 1.
Let's assume that V3/4 is a rational number and can be written as a fraction p/q, where p and q are integers and have no common factors other than 1.
Then, by squaring both sides, we get:
(V3/4)^2 = (p/q)^2
3/16 = p^2/q^2
Cross-multiplying, we have:
3q^2 = 16p^2
From this equation, we can observe that since 3 is a prime number, it should also be a factor on the left side of the equation. However, this is not the case for 16p^2. This implies that 3 cannot be a factor of 16p^2, which contradicts our assumption that p/q is a fraction with no common factors other than 1.
Therefore, V3/4 cannot be expressed as a fraction of two integers, indicating that it is an irrational number.
To determine if V3/4 is rational or irrational, we need to check if we can simplify it into a fraction of two integers.
To simplify V3/4, we need to find a fraction where the numerator and denominator have no common factors other than 1.
Let's assume that V3/4 is a rational number and can be written as a fraction p/q, where p and q are integers and have no common factors other than 1.
Then, by squaring both sides, we get:
(V3/4)^2 = (p/q)^2
3/16 = p^2/q^2
Cross-multiplying, we have:
3q^2 = 16p^2
From this equation, we can observe that since 3 is a prime number, it should also be a factor on the left side of the equation. However, this is not the case for 16p^2. This implies that 3 cannot be a factor of 16p^2, which contradicts our assumption that p/q is a fraction with no common factors other than 1.
Therefore, V3/4 cannot be expressed as a fraction of two integers, indicating that it is an irrational number.
1 answer