Question

how to find rational numbers between 1/2 and √2​

Answer 1

Answer:

4/3 and 5/3

Explanation:

1 = 1/1 = (1×3) / (1×3) = 3/3

2 = 2/1 = (2×3) / (1×3) = 6/3

Hence, 4/3 and 5/3 are two rational numbers between 1 and 2.

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Answer 2

The rational number between a and b is (a + b)/2

Hence rational number between 1 and 2 is (1+2)/2 = 3/2 = 1.5

Rational number between 1 and 3/2 is [1+(3/2)]/2 = 5/4 = 1.25

Rational number between 1 and 5/4 is [1+(5/4)]/2 = 9/8 = 1.125

Rational number between 3/2 and 2 is [(3/2) + 2]/2 = 7/4= 1.75

Therefore four rational numbers between 1 and 2 are 9/8, 5/4, 3/2, and 7/4

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