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find the four irrational numbers between the given two rationals. (a) 3/5,5/3
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Most Upvoted Answer
find the four irrational numbers between the given two rationals. (a) ...
3/5,5/3,
3×3/5×3,5×5/3×5,
9/15,25/15,
10/15,11/15,12/15,13/15, etc.
3×3/5×3,5×5/3×5,
9/15,25/15,
10/15,11/15,12/15,13/15, etc.
Community Answer
find the four irrational numbers between the given two rationals. (a) ...
To find the four irrational numbers between 3/5 and 5/3, we need to find four numbers that are greater than 3/5 and less than 5/3, but are not rational numbers.
One way to find such numbers is to take the average of the two given rational numbers and then add or subtract a small irrational number. Let's call the two given rational numbers a and b.
In this case, a = 3/5 and b = 5/3.
The average of a and b is:
(a + b) / 2 = (3/5 + 5/3) / 2 = (9/15 + 25/15) / 2 = 34/15 / 2 = 34/30 = 17/15.
Now we can add or subtract a small irrational number to this average to find the four irrational numbers between 3/5 and 5/3.
One example is to add or subtract the square root of 2 (since √2 is irrational).
So the four irrational numbers between 3/5 and 5/3 are:
1) (a + b) / 2 - √2 = 17/15 - √2
2) (a + b) / 2 + √2 = 17/15 + √2
3) (a + b) / 2 - √2 = 17/15 - √2
4) (a + b) / 2 + √2 = 17/15 + √2
Note: There are infinitely many irrational numbers between any two rational numbers, so these are just four examples.
One way to find such numbers is to take the average of the two given rational numbers and then add or subtract a small irrational number. Let's call the two given rational numbers a and b.
In this case, a = 3/5 and b = 5/3.
The average of a and b is:
(a + b) / 2 = (3/5 + 5/3) / 2 = (9/15 + 25/15) / 2 = 34/15 / 2 = 34/30 = 17/15.
Now we can add or subtract a small irrational number to this average to find the four irrational numbers between 3/5 and 5/3.
One example is to add or subtract the square root of 2 (since √2 is irrational).
So the four irrational numbers between 3/5 and 5/3 are:
1) (a + b) / 2 - √2 = 17/15 - √2
2) (a + b) / 2 + √2 = 17/15 + √2
3) (a + b) / 2 - √2 = 17/15 - √2
4) (a + b) / 2 + √2 = 17/15 + √2
Note: There are infinitely many irrational numbers between any two rational numbers, so these are just four examples.
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find the four irrational numbers between the given two rationals. (a) 3/5,5/3 Related: Number System- Rational Numbers & Real Numbers?
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