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find the four irrational numbers between the given two rationals. (a) 3/5,5/3
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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.
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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.
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